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Simplifying 10x(x + -1) = 360 Reorder the terms: 10x(-1 + x) = 360 (-1 * 10x + x * 10x) = 360 (-10x + 10x2) = 360 Solving -10x + 10x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + -10x + 10x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + -10x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-36 + -1x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-36 + -1x + x2)' equal to zero and attempt to solve: Simplifying -36 + -1x + x2 = 0 Solving -36 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -1x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -1x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1x + x2 = 0 + 36 -1x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1x + x2 = 36 The x term is -1x. 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. -1x + 0.25 + x2 = 36 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 0.25 + -1x + x2 = 36.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -0.5 = 6.020797289 Simplifying x + -0.5 = 6.020797289 Reorder the terms: -0.5 + x = 6.020797289 Solving -0.5 + x = 6.020797289 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 = 6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.020797289 + 0.5 x = 6.020797289 + 0.5 Combine like terms: 6.020797289 + 0.5 = 6.520797289 x = 6.520797289 Simplifying x = 6.520797289Subproblem 2
x + -0.5 = -6.020797289 Simplifying x + -0.5 = -6.020797289 Reorder the terms: -0.5 + x = -6.020797289 Solving -0.5 + x = -6.020797289 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 = -6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.020797289 + 0.5 x = -6.020797289 + 0.5 Combine like terms: -6.020797289 + 0.5 = -5.520797289 x = -5.520797289 Simplifying x = -5.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.520797289, -5.520797289}Solution
x = {6.520797289, -5.520797289}
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