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Simplifying 10x2 = 1740x + -12600 Reorder the terms: 10x2 = -12600 + 1740x Solving 10x2 = -12600 + 1740x Solving for variable 'x'. Reorder the terms: 12600 + -1740x + 10x2 = -12600 + 1740x + 12600 + -1740x Reorder the terms: 12600 + -1740x + 10x2 = -12600 + 12600 + 1740x + -1740x Combine like terms: -12600 + 12600 = 0 12600 + -1740x + 10x2 = 0 + 1740x + -1740x 12600 + -1740x + 10x2 = 1740x + -1740x Combine like terms: 1740x + -1740x = 0 12600 + -1740x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(1260 + -174x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(1260 + -174x + x2)' equal to zero and attempt to solve: Simplifying 1260 + -174x + x2 = 0 Solving 1260 + -174x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1260' to each side of the equation. 1260 + -174x + -1260 + x2 = 0 + -1260 Reorder the terms: 1260 + -1260 + -174x + x2 = 0 + -1260 Combine like terms: 1260 + -1260 = 0 0 + -174x + x2 = 0 + -1260 -174x + x2 = 0 + -1260 Combine like terms: 0 + -1260 = -1260 -174x + x2 = -1260 The x term is -174x. Take half its coefficient (-87). Square it (7569) and add it to both sides. Add '7569' to each side of the equation. -174x + 7569 + x2 = -1260 + 7569 Reorder the terms: 7569 + -174x + x2 = -1260 + 7569 Combine like terms: -1260 + 7569 = 6309 7569 + -174x + x2 = 6309 Factor a perfect square on the left side: (x + -87)(x + -87) = 6309 Calculate the square root of the right side: 79.429213769 Break this problem into two subproblems by setting (x + -87) equal to 79.429213769 and -79.429213769.Subproblem 1
x + -87 = 79.429213769 Simplifying x + -87 = 79.429213769 Reorder the terms: -87 + x = 79.429213769 Solving -87 + x = 79.429213769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87' to each side of the equation. -87 + 87 + x = 79.429213769 + 87 Combine like terms: -87 + 87 = 0 0 + x = 79.429213769 + 87 x = 79.429213769 + 87 Combine like terms: 79.429213769 + 87 = 166.429213769 x = 166.429213769 Simplifying x = 166.429213769Subproblem 2
x + -87 = -79.429213769 Simplifying x + -87 = -79.429213769 Reorder the terms: -87 + x = -79.429213769 Solving -87 + x = -79.429213769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '87' to each side of the equation. -87 + 87 + x = -79.429213769 + 87 Combine like terms: -87 + 87 = 0 0 + x = -79.429213769 + 87 x = -79.429213769 + 87 Combine like terms: -79.429213769 + 87 = 7.570786231 x = 7.570786231 Simplifying x = 7.570786231Solution
The solution to the problem is based on the solutions from the subproblems. x = {166.429213769, 7.570786231}Solution
x = {166.429213769, 7.570786231}
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