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Simplifying 3x(x + -5) + 7 = 2x(x + 4) + 6 Reorder the terms: 3x(-5 + x) + 7 = 2x(x + 4) + 6 (-5 * 3x + x * 3x) + 7 = 2x(x + 4) + 6 (-15x + 3x2) + 7 = 2x(x + 4) + 6 Reorder the terms: 7 + -15x + 3x2 = 2x(x + 4) + 6 Reorder the terms: 7 + -15x + 3x2 = 2x(4 + x) + 6 7 + -15x + 3x2 = (4 * 2x + x * 2x) + 6 7 + -15x + 3x2 = (8x + 2x2) + 6 Reorder the terms: 7 + -15x + 3x2 = 6 + 8x + 2x2 Solving 7 + -15x + 3x2 = 6 + 8x + 2x2 Solving for variable 'x'. Reorder the terms: 7 + -6 + -15x + -8x + 3x2 + -2x2 = 6 + 8x + 2x2 + -6 + -8x + -2x2 Combine like terms: 7 + -6 = 1 1 + -15x + -8x + 3x2 + -2x2 = 6 + 8x + 2x2 + -6 + -8x + -2x2 Combine like terms: -15x + -8x = -23x 1 + -23x + 3x2 + -2x2 = 6 + 8x + 2x2 + -6 + -8x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 1 + -23x + 1x2 = 6 + 8x + 2x2 + -6 + -8x + -2x2 Reorder the terms: 1 + -23x + 1x2 = 6 + -6 + 8x + -8x + 2x2 + -2x2 Combine like terms: 6 + -6 = 0 1 + -23x + 1x2 = 0 + 8x + -8x + 2x2 + -2x2 1 + -23x + 1x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 1 + -23x + 1x2 = 0 + 2x2 + -2x2 1 + -23x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1 + -23x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -23x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -23x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -23x + x2 = 0 + -1 -23x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -23x + x2 = -1 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -1 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -1 + 132.25 Combine like terms: -1 + 132.25 = 131.25 132.25 + -23x + x2 = 131.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (x + -11.5) equal to 11.456439237 and -11.456439237.Subproblem 1
x + -11.5 = 11.456439237 Simplifying x + -11.5 = 11.456439237 Reorder the terms: -11.5 + x = 11.456439237 Solving -11.5 + x = 11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 11.456439237 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.456439237 + 11.5 x = 11.456439237 + 11.5 Combine like terms: 11.456439237 + 11.5 = 22.956439237 x = 22.956439237 Simplifying x = 22.956439237Subproblem 2
x + -11.5 = -11.456439237 Simplifying x + -11.5 = -11.456439237 Reorder the terms: -11.5 + x = -11.456439237 Solving -11.5 + x = -11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -11.456439237 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.456439237 + 11.5 x = -11.456439237 + 11.5 Combine like terms: -11.456439237 + 11.5 = 0.043560763 x = 0.043560763 Simplifying x = 0.043560763Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.956439237, 0.043560763}
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