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Simplifying -1[7x + -1(2x + 2)] = -5 + -1[3(3x + -4) * 2x] Reorder the terms: -1[7x + -1(2 + 2x)] = -5 + -1[3(3x + -4) * 2x] -1[7x + (2 * -1 + 2x * -1)] = -5 + -1[3(3x + -4) * 2x] -1[7x + (-2 + -2x)] = -5 + -1[3(3x + -4) * 2x] Reorder the terms: -1[-2 + 7x + -2x] = -5 + -1[3(3x + -4) * 2x] Combine like terms: 7x + -2x = 5x -1[-2 + 5x] = -5 + -1[3(3x + -4) * 2x] [-2 * -1 + 5x * -1] = -5 + -1[3(3x + -4) * 2x] [2 + -5x] = -5 + -1[3(3x + -4) * 2x] Reorder the terms: 2 + -5x = -5 + -1[3(-4 + 3x) * 2x] Reorder the terms for easier multiplication: 2 + -5x = -5 + -1[3 * 2x(-4 + 3x)] Multiply 3 * 2 2 + -5x = -5 + -1[6x(-4 + 3x)] 2 + -5x = -5 + -1[(-4 * 6x + 3x * 6x)] 2 + -5x = -5 + -1[(-24x + 18x2)] 2 + -5x = -5 + [-24x * -1 + 18x2 * -1] 2 + -5x = -5 + [24x + -18x2] Solving 2 + -5x = -5 + 24x + -18x2 Solving for variable 'x'. Reorder the terms: 2 + 5 + -5x + -24x + 18x2 = -5 + 24x + -18x2 + 5 + -24x + 18x2 Combine like terms: 2 + 5 = 7 7 + -5x + -24x + 18x2 = -5 + 24x + -18x2 + 5 + -24x + 18x2 Combine like terms: -5x + -24x = -29x 7 + -29x + 18x2 = -5 + 24x + -18x2 + 5 + -24x + 18x2 Reorder the terms: 7 + -29x + 18x2 = -5 + 5 + 24x + -24x + -18x2 + 18x2 Combine like terms: -5 + 5 = 0 7 + -29x + 18x2 = 0 + 24x + -24x + -18x2 + 18x2 7 + -29x + 18x2 = 24x + -24x + -18x2 + 18x2 Combine like terms: 24x + -24x = 0 7 + -29x + 18x2 = 0 + -18x2 + 18x2 7 + -29x + 18x2 = -18x2 + 18x2 Combine like terms: -18x2 + 18x2 = 0 7 + -29x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.3888888889 + -1.611111111x + x2 = 0 Move the constant term to the right: Add '-0.3888888889' to each side of the equation. 0.3888888889 + -1.611111111x + -0.3888888889 + x2 = 0 + -0.3888888889 Reorder the terms: 0.3888888889 + -0.3888888889 + -1.611111111x + x2 = 0 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + -1.611111111x + x2 = 0 + -0.3888888889 -1.611111111x + x2 = 0 + -0.3888888889 Combine like terms: 0 + -0.3888888889 = -0.3888888889 -1.611111111x + x2 = -0.3888888889 The x term is -1.611111111x. Take half its coefficient (-0.8055555555). Square it (0.6489197530) and add it to both sides. Add '0.6489197530' to each side of the equation. -1.611111111x + 0.6489197530 + x2 = -0.3888888889 + 0.6489197530 Reorder the terms: 0.6489197530 + -1.611111111x + x2 = -0.3888888889 + 0.6489197530 Combine like terms: -0.3888888889 + 0.6489197530 = 0.2600308641 0.6489197530 + -1.611111111x + x2 = 0.2600308641 Factor a perfect square on the left side: (x + -0.8055555555)(x + -0.8055555555) = 0.2600308641 Calculate the square root of the right side: 0.509932215 Break this problem into two subproblems by setting (x + -0.8055555555) equal to 0.509932215 and -0.509932215.Subproblem 1
x + -0.8055555555 = 0.509932215 Simplifying x + -0.8055555555 = 0.509932215 Reorder the terms: -0.8055555555 + x = 0.509932215 Solving -0.8055555555 + x = 0.509932215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8055555555' to each side of the equation. -0.8055555555 + 0.8055555555 + x = 0.509932215 + 0.8055555555 Combine like terms: -0.8055555555 + 0.8055555555 = 0.0000000000 0.0000000000 + x = 0.509932215 + 0.8055555555 x = 0.509932215 + 0.8055555555 Combine like terms: 0.509932215 + 0.8055555555 = 1.3154877705 x = 1.3154877705 Simplifying x = 1.3154877705Subproblem 2
x + -0.8055555555 = -0.509932215 Simplifying x + -0.8055555555 = -0.509932215 Reorder the terms: -0.8055555555 + x = -0.509932215 Solving -0.8055555555 + x = -0.509932215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8055555555' to each side of the equation. -0.8055555555 + 0.8055555555 + x = -0.509932215 + 0.8055555555 Combine like terms: -0.8055555555 + 0.8055555555 = 0.0000000000 0.0000000000 + x = -0.509932215 + 0.8055555555 x = -0.509932215 + 0.8055555555 Combine like terms: -0.509932215 + 0.8055555555 = 0.2956233405 x = 0.2956233405 Simplifying x = 0.2956233405Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3154877705, 0.2956233405}
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