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Simplifying 900 = 5[x(x + 14)] Reorder the terms: 900 = 5[x(14 + x)] 900 = 5[(14 * x + x * x)] 900 = 5[(14x + x2)] 900 = [14x * 5 + x2 * 5] 900 = [70x + 5x2] Solving 900 = 70x + 5x2 Solving for variable 'x'. Reorder the terms: 900 + -70x + -5x2 = 70x + -70x + 5x2 + -5x2 Combine like terms: 70x + -70x = 0 900 + -70x + -5x2 = 0 + 5x2 + -5x2 900 + -70x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 900 + -70x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(180 + -14x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(180 + -14x + -1x2)' equal to zero and attempt to solve: Simplifying 180 + -14x + -1x2 = 0 Solving 180 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -180 + 14x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 14x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 14x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 14x + x2 = 0 + 180 14x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 14x + x2 = 180 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 180 + 49 Reorder the terms: 49 + 14x + x2 = 180 + 49 Combine like terms: 180 + 49 = 229 49 + 14x + x2 = 229 Factor a perfect square on the left side: (x + 7)(x + 7) = 229 Calculate the square root of the right side: 15.13274595 Break this problem into two subproblems by setting (x + 7) equal to 15.13274595 and -15.13274595.Subproblem 1
x + 7 = 15.13274595 Simplifying x + 7 = 15.13274595 Reorder the terms: 7 + x = 15.13274595 Solving 7 + x = 15.13274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 15.13274595 + -7 Combine like terms: 7 + -7 = 0 0 + x = 15.13274595 + -7 x = 15.13274595 + -7 Combine like terms: 15.13274595 + -7 = 8.13274595 x = 8.13274595 Simplifying x = 8.13274595Subproblem 2
x + 7 = -15.13274595 Simplifying x + 7 = -15.13274595 Reorder the terms: 7 + x = -15.13274595 Solving 7 + x = -15.13274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -15.13274595 + -7 Combine like terms: 7 + -7 = 0 0 + x = -15.13274595 + -7 x = -15.13274595 + -7 Combine like terms: -15.13274595 + -7 = -22.13274595 x = -22.13274595 Simplifying x = -22.13274595Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.13274595, -22.13274595}Solution
x = {8.13274595, -22.13274595}
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