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Simplifying 15x2 + 18x + -270 = 0 Reorder the terms: -270 + 18x + 15x2 = 0 Solving -270 + 18x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-90 + 6x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-90 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying -90 + 6x + 5x2 = 0 Solving -90 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18 + 1.2x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 1.2x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 1.2x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 1.2x + x2 = 0 + 18 1.2x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 1.2x + x2 = 18 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 18 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 18 + 0.36 Combine like terms: 18 + 0.36 = 18.36 0.36 + 1.2x + x2 = 18.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 18.36 Calculate the square root of the right side: 4.284857057 Break this problem into two subproblems by setting (x + 0.6) equal to 4.284857057 and -4.284857057.Subproblem 1
x + 0.6 = 4.284857057 Simplifying x + 0.6 = 4.284857057 Reorder the terms: 0.6 + x = 4.284857057 Solving 0.6 + x = 4.284857057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 4.284857057 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 4.284857057 + -0.6 x = 4.284857057 + -0.6 Combine like terms: 4.284857057 + -0.6 = 3.684857057 x = 3.684857057 Simplifying x = 3.684857057Subproblem 2
x + 0.6 = -4.284857057 Simplifying x + 0.6 = -4.284857057 Reorder the terms: 0.6 + x = -4.284857057 Solving 0.6 + x = -4.284857057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -4.284857057 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -4.284857057 + -0.6 x = -4.284857057 + -0.6 Combine like terms: -4.284857057 + -0.6 = -4.884857057 x = -4.884857057 Simplifying x = -4.884857057Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.684857057, -4.884857057}Solution
x = {3.684857057, -4.884857057}
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