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Simplifying -2(x + -2) + -7x = 4(-2x + -3) * 5x Reorder the terms: -2(-2 + x) + -7x = 4(-2x + -3) * 5x (-2 * -2 + x * -2) + -7x = 4(-2x + -3) * 5x (4 + -2x) + -7x = 4(-2x + -3) * 5x Combine like terms: -2x + -7x = -9x 4 + -9x = 4(-2x + -3) * 5x Reorder the terms: 4 + -9x = 4(-3 + -2x) * 5x Reorder the terms for easier multiplication: 4 + -9x = 4 * 5x(-3 + -2x) Multiply 4 * 5 4 + -9x = 20x(-3 + -2x) 4 + -9x = (-3 * 20x + -2x * 20x) 4 + -9x = (-60x + -40x2) Solving 4 + -9x = -60x + -40x2 Solving for variable 'x'. Combine like terms: -9x + 60x = 51x 4 + 51x + 40x2 = -60x + -40x2 + 60x + 40x2 Reorder the terms: 4 + 51x + 40x2 = -60x + 60x + -40x2 + 40x2 Combine like terms: -60x + 60x = 0 4 + 51x + 40x2 = 0 + -40x2 + 40x2 4 + 51x + 40x2 = -40x2 + 40x2 Combine like terms: -40x2 + 40x2 = 0 4 + 51x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.1 + 1.275x + x2 = 0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 1.275x + -0.1 + x2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + 1.275x + x2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 1.275x + x2 = 0 + -0.1 1.275x + x2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 1.275x + x2 = -0.1 The x term is 1.275x. Take half its coefficient (0.6375). Square it (0.40640625) and add it to both sides. Add '0.40640625' to each side of the equation. 1.275x + 0.40640625 + x2 = -0.1 + 0.40640625 Reorder the terms: 0.40640625 + 1.275x + x2 = -0.1 + 0.40640625 Combine like terms: -0.1 + 0.40640625 = 0.30640625 0.40640625 + 1.275x + x2 = 0.30640625 Factor a perfect square on the left side: (x + 0.6375)(x + 0.6375) = 0.30640625 Calculate the square root of the right side: 0.553539746 Break this problem into two subproblems by setting (x + 0.6375) equal to 0.553539746 and -0.553539746.Subproblem 1
x + 0.6375 = 0.553539746 Simplifying x + 0.6375 = 0.553539746 Reorder the terms: 0.6375 + x = 0.553539746 Solving 0.6375 + x = 0.553539746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6375' to each side of the equation. 0.6375 + -0.6375 + x = 0.553539746 + -0.6375 Combine like terms: 0.6375 + -0.6375 = 0.0000 0.0000 + x = 0.553539746 + -0.6375 x = 0.553539746 + -0.6375 Combine like terms: 0.553539746 + -0.6375 = -0.083960254 x = -0.083960254 Simplifying x = -0.083960254Subproblem 2
x + 0.6375 = -0.553539746 Simplifying x + 0.6375 = -0.553539746 Reorder the terms: 0.6375 + x = -0.553539746 Solving 0.6375 + x = -0.553539746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6375' to each side of the equation. 0.6375 + -0.6375 + x = -0.553539746 + -0.6375 Combine like terms: 0.6375 + -0.6375 = 0.0000 0.0000 + x = -0.553539746 + -0.6375 x = -0.553539746 + -0.6375 Combine like terms: -0.553539746 + -0.6375 = -1.191039746 x = -1.191039746 Simplifying x = -1.191039746Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.083960254, -1.191039746}
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