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Simplifying 15x2 + 18 + -270x = 0 Reorder the terms: 18 + -270x + 15x2 = 0 Solving 18 + -270x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -90x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -90x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + -90x + 5x2 = 0 Solving 6 + -90x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -18x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -18x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -18x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -18x + x2 = 0 + -1.2 -18x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -18x + x2 = -1.2 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -1.2 + 81 Reorder the terms: 81 + -18x + x2 = -1.2 + 81 Combine like terms: -1.2 + 81 = 79.8 81 + -18x + x2 = 79.8 Factor a perfect square on the left side: (x + -9)(x + -9) = 79.8 Calculate the square root of the right side: 8.933084574 Break this problem into two subproblems by setting (x + -9) equal to 8.933084574 and -8.933084574.Subproblem 1
x + -9 = 8.933084574 Simplifying x + -9 = 8.933084574 Reorder the terms: -9 + x = 8.933084574 Solving -9 + x = 8.933084574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 8.933084574 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.933084574 + 9 x = 8.933084574 + 9 Combine like terms: 8.933084574 + 9 = 17.933084574 x = 17.933084574 Simplifying x = 17.933084574Subproblem 2
x + -9 = -8.933084574 Simplifying x + -9 = -8.933084574 Reorder the terms: -9 + x = -8.933084574 Solving -9 + x = -8.933084574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -8.933084574 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.933084574 + 9 x = -8.933084574 + 9 Combine like terms: -8.933084574 + 9 = 0.066915426 x = 0.066915426 Simplifying x = 0.066915426Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.933084574, 0.066915426}Solution
x = {17.933084574, 0.066915426}
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