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Simplifying 2(-1x + 3x) * 3(-1x) + 7 = (-1x) + (-3) Combine like terms: -1x + 3x = 2x 2(2x) * 3(-1x) + 7 = (-1x) + (-3) Remove parenthesis around (2x) 2 * 2x * 3(-1x) + 7 = (-1x) + (-3) Remove parenthesis around (-1x) 2 * 2x * 3 * -1x + 7 = (-1x) + (-3) Reorder the terms for easier multiplication: 2 * 2 * 3 * -1x * x + 7 = (-1x) + (-3) Multiply 2 * 2 4 * 3 * -1x * x + 7 = (-1x) + (-3) Multiply 4 * 3 12 * -1x * x + 7 = (-1x) + (-3) Multiply 12 * -1 -12x * x + 7 = (-1x) + (-3) Multiply x * x -12x2 + 7 = (-1x) + (-3) Reorder the terms: 7 + -12x2 = (-1x) + (-3) 7 + -12x2 = (-1x) + -3 Reorder the terms: 7 + -12x2 = -3 + (-1x) Solving 7 + -12x2 = -3 + (-1x) Solving for variable 'x'. 7 + -12x2 + 3 + x = -3 + (-1x) + 3 + (x) Reorder the terms: 7 + 3 + x + -12x2 = -3 + (-1x) + 3 + (x) Combine like terms: 7 + 3 = 10 10 + x + -12x2 = -3 + (-1x) + 3 + (x) 10 + x + -12x2 = -3 + (-1x) + 3 + x Reorder the terms: 10 + x + -12x2 = -3 + 3 + (-1x) + x Combine like terms: -3 + 3 = 0 10 + x + -12x2 = 0 + (-1x) + x 10 + x + -12x2 = (-1x) + x Combine like terms: (-1x) + x = 0 10 + x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.8333333333 + -0.08333333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -0.08333333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -0.08333333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -0.08333333333x + x2 = 0 + 0.8333333333 -0.08333333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -0.08333333333x + x2 = 0.8333333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.08333333333x + 0.25 + x2 = 0.8333333333 + 0.25 Reorder the terms: 0.25 + -0.08333333333x + x2 = 0.8333333333 + 0.25 Combine like terms: 0.8333333333 + 0.25 = 1.0833333333 0.25 + -0.08333333333x + x2 = 1.0833333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.0833333333 Calculate the square root of the right side: 1.040833 Break this problem into two subproblems by setting (x + 0.5) equal to 1.040833 and -1.040833.Subproblem 1
x + 0.5 = 1.040833 Simplifying x + 0.5 = 1.040833 Reorder the terms: 0.5 + x = 1.040833 Solving 0.5 + x = 1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.040833 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.040833 + -0.5 x = 1.040833 + -0.5 Combine like terms: 1.040833 + -0.5 = 0.540833 x = 0.540833 Simplifying x = 0.540833Subproblem 2
x + 0.5 = -1.040833 Simplifying x + 0.5 = -1.040833 Reorder the terms: 0.5 + x = -1.040833 Solving 0.5 + x = -1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.040833 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.040833 + -0.5 x = -1.040833 + -0.5 Combine like terms: -1.040833 + -0.5 = -1.540833 x = -1.540833 Simplifying x = -1.540833Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.540833, -1.540833}
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