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Simplifying 4x2 + 64x = 360 Reorder the terms: 64x + 4x2 = 360 Solving 64x + 4x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 64x + 4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 64x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-90 + 16x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-90 + 16x + x2)' equal to zero and attempt to solve: Simplifying -90 + 16x + x2 = 0 Solving -90 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 16x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 16x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 16x + x2 = 0 + 90 16x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 16x + x2 = 90 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 90 + 64 Reorder the terms: 64 + 16x + x2 = 90 + 64 Combine like terms: 90 + 64 = 154 64 + 16x + x2 = 154 Factor a perfect square on the left side: (x + 8)(x + 8) = 154 Calculate the square root of the right side: 12.409673646 Break this problem into two subproblems by setting (x + 8) equal to 12.409673646 and -12.409673646.Subproblem 1
x + 8 = 12.409673646 Simplifying x + 8 = 12.409673646 Reorder the terms: 8 + x = 12.409673646 Solving 8 + x = 12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 12.409673646 + -8 Combine like terms: 8 + -8 = 0 0 + x = 12.409673646 + -8 x = 12.409673646 + -8 Combine like terms: 12.409673646 + -8 = 4.409673646 x = 4.409673646 Simplifying x = 4.409673646Subproblem 2
x + 8 = -12.409673646 Simplifying x + 8 = -12.409673646 Reorder the terms: 8 + x = -12.409673646 Solving 8 + x = -12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -12.409673646 + -8 Combine like terms: 8 + -8 = 0 0 + x = -12.409673646 + -8 x = -12.409673646 + -8 Combine like terms: -12.409673646 + -8 = -20.409673646 x = -20.409673646 Simplifying x = -20.409673646Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.409673646, -20.409673646}Solution
x = {4.409673646, -20.409673646}
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