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Simplifying x(10x + 10) = 1500 Reorder the terms: x(10 + 10x) = 1500 (10 * x + 10x * x) = 1500 (10x + 10x2) = 1500 Solving 10x + 10x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 10x + 10x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 10x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-150 + x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-150 + x + x2)' equal to zero and attempt to solve: Simplifying -150 + x + x2 = 0 Solving -150 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + x + x2 = 0 + 150 x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 x + x2 = 150 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. x + 0.25 + x2 = 150 + 0.25 Reorder the terms: 0.25 + x + x2 = 150 + 0.25 Combine like terms: 150 + 0.25 = 150.25 0.25 + x + x2 = 150.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 150.25 Calculate the square root of the right side: 12.257650672 Break this problem into two subproblems by setting (x + 0.5) equal to 12.257650672 and -12.257650672.Subproblem 1
x + 0.5 = 12.257650672 Simplifying x + 0.5 = 12.257650672 Reorder the terms: 0.5 + x = 12.257650672 Solving 0.5 + x = 12.257650672 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 = 12.257650672 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.257650672 + -0.5 x = 12.257650672 + -0.5 Combine like terms: 12.257650672 + -0.5 = 11.757650672 x = 11.757650672 Simplifying x = 11.757650672Subproblem 2
x + 0.5 = -12.257650672 Simplifying x + 0.5 = -12.257650672 Reorder the terms: 0.5 + x = -12.257650672 Solving 0.5 + x = -12.257650672 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 = -12.257650672 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.257650672 + -0.5 x = -12.257650672 + -0.5 Combine like terms: -12.257650672 + -0.5 = -12.757650672 x = -12.757650672 Simplifying x = -12.757650672Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.757650672, -12.757650672}Solution
x = {11.757650672, -12.757650672}
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