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Simplifying 9x(225 + -14x) = 180 (225 * 9x + -14x * 9x) = 180 (2025x + -126x2) = 180 Solving 2025x + -126x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 2025x + -126x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 2025x + -126x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-20 + 225x + -14x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-20 + 225x + -14x2)' equal to zero and attempt to solve: Simplifying -20 + 225x + -14x2 = 0 Solving -20 + 225x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. 1.428571429 + -16.07142857x + x2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + -16.07142857x + -1.428571429 + x2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + -16.07142857x + x2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + -16.07142857x + x2 = 0 + -1.428571429 -16.07142857x + x2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 -16.07142857x + x2 = -1.428571429 The x term is -16.07142857x. Take half its coefficient (-8.035714285). Square it (64.57270407) and add it to both sides. Add '64.57270407' to each side of the equation. -16.07142857x + 64.57270407 + x2 = -1.428571429 + 64.57270407 Reorder the terms: 64.57270407 + -16.07142857x + x2 = -1.428571429 + 64.57270407 Combine like terms: -1.428571429 + 64.57270407 = 63.144132641 64.57270407 + -16.07142857x + x2 = 63.144132641 Factor a perfect square on the left side: (x + -8.035714285)(x + -8.035714285) = 63.144132641 Calculate the square root of the right side: 7.946328249 Break this problem into two subproblems by setting (x + -8.035714285) equal to 7.946328249 and -7.946328249.Subproblem 1
x + -8.035714285 = 7.946328249 Simplifying x + -8.035714285 = 7.946328249 Reorder the terms: -8.035714285 + x = 7.946328249 Solving -8.035714285 + x = 7.946328249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.035714285' to each side of the equation. -8.035714285 + 8.035714285 + x = 7.946328249 + 8.035714285 Combine like terms: -8.035714285 + 8.035714285 = 0.000000000 0.000000000 + x = 7.946328249 + 8.035714285 x = 7.946328249 + 8.035714285 Combine like terms: 7.946328249 + 8.035714285 = 15.982042534 x = 15.982042534 Simplifying x = 15.982042534Subproblem 2
x + -8.035714285 = -7.946328249 Simplifying x + -8.035714285 = -7.946328249 Reorder the terms: -8.035714285 + x = -7.946328249 Solving -8.035714285 + x = -7.946328249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.035714285' to each side of the equation. -8.035714285 + 8.035714285 + x = -7.946328249 + 8.035714285 Combine like terms: -8.035714285 + 8.035714285 = 0.000000000 0.000000000 + x = -7.946328249 + 8.035714285 x = -7.946328249 + 8.035714285 Combine like terms: -7.946328249 + 8.035714285 = 0.089386036 x = 0.089386036 Simplifying x = 0.089386036Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.982042534, 0.089386036}Solution
x = {15.982042534, 0.089386036}
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