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Simplifying 4x2 + 16x = 600 Reorder the terms: 16x + 4x2 = 600 Solving 16x + 4x2 = 600 Solving for variable 'x'. Reorder the terms: -600 + 16x + 4x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-150 + 4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-150 + 4x + x2)' equal to zero and attempt to solve: Simplifying -150 + 4x + x2 = 0 Solving -150 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 4x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 4x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 4x + x2 = 0 + 150 4x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 4x + x2 = 150 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 150 + 4 Reorder the terms: 4 + 4x + x2 = 150 + 4 Combine like terms: 150 + 4 = 154 4 + 4x + x2 = 154 Factor a perfect square on the left side: (x + 2)(x + 2) = 154 Calculate the square root of the right side: 12.409673646 Break this problem into two subproblems by setting (x + 2) equal to 12.409673646 and -12.409673646.Subproblem 1
x + 2 = 12.409673646 Simplifying x + 2 = 12.409673646 Reorder the terms: 2 + x = 12.409673646 Solving 2 + x = 12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 12.409673646 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.409673646 + -2 x = 12.409673646 + -2 Combine like terms: 12.409673646 + -2 = 10.409673646 x = 10.409673646 Simplifying x = 10.409673646Subproblem 2
x + 2 = -12.409673646 Simplifying x + 2 = -12.409673646 Reorder the terms: 2 + x = -12.409673646 Solving 2 + x = -12.409673646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -12.409673646 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.409673646 + -2 x = -12.409673646 + -2 Combine like terms: -12.409673646 + -2 = -14.409673646 x = -14.409673646 Simplifying x = -14.409673646Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.409673646, -14.409673646}Solution
x = {10.409673646, -14.409673646}
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