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Simplifying 1500 = -3x2 + 630x Reorder the terms: 1500 = 630x + -3x2 Solving 1500 = 630x + -3x2 Solving for variable 'x'. Reorder the terms: 1500 + -630x + 3x2 = 630x + -630x + -3x2 + 3x2 Combine like terms: 630x + -630x = 0 1500 + -630x + 3x2 = 0 + -3x2 + 3x2 1500 + -630x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 1500 + -630x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(500 + -210x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(500 + -210x + x2)' equal to zero and attempt to solve: Simplifying 500 + -210x + x2 = 0 Solving 500 + -210x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + -210x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -210x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -210x + x2 = 0 + -500 -210x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -210x + x2 = -500 The x term is -210x. Take half its coefficient (-105). Square it (11025) and add it to both sides. Add '11025' to each side of the equation. -210x + 11025 + x2 = -500 + 11025 Reorder the terms: 11025 + -210x + x2 = -500 + 11025 Combine like terms: -500 + 11025 = 10525 11025 + -210x + x2 = 10525 Factor a perfect square on the left side: (x + -105)(x + -105) = 10525 Calculate the square root of the right side: 102.591422643 Break this problem into two subproblems by setting (x + -105) equal to 102.591422643 and -102.591422643.Subproblem 1
x + -105 = 102.591422643 Simplifying x + -105 = 102.591422643 Reorder the terms: -105 + x = 102.591422643 Solving -105 + x = 102.591422643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + x = 102.591422643 + 105 Combine like terms: -105 + 105 = 0 0 + x = 102.591422643 + 105 x = 102.591422643 + 105 Combine like terms: 102.591422643 + 105 = 207.591422643 x = 207.591422643 Simplifying x = 207.591422643Subproblem 2
x + -105 = -102.591422643 Simplifying x + -105 = -102.591422643 Reorder the terms: -105 + x = -102.591422643 Solving -105 + x = -102.591422643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + x = -102.591422643 + 105 Combine like terms: -105 + 105 = 0 0 + x = -102.591422643 + 105 x = -102.591422643 + 105 Combine like terms: -102.591422643 + 105 = 2.408577357 x = 2.408577357 Simplifying x = 2.408577357Solution
The solution to the problem is based on the solutions from the subproblems. x = {207.591422643, 2.408577357}Solution
x = {207.591422643, 2.408577357}
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