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Simplifying 15x2 + -30x + -114 = 0 Reorder the terms: -114 + -30x + 15x2 = 0 Solving -114 + -30x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-38 + -10x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-38 + -10x + 5x2)' equal to zero and attempt to solve: Simplifying -38 + -10x + 5x2 = 0 Solving -38 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.6 + -2x + x2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + -2x + 7.6 + x2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + -2x + x2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + -2x + x2 = 0 + 7.6 -2x + x2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 -2x + x2 = 7.6 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 7.6 + 1 Reorder the terms: 1 + -2x + x2 = 7.6 + 1 Combine like terms: 7.6 + 1 = 8.6 1 + -2x + x2 = 8.6 Factor a perfect square on the left side: (x + -1)(x + -1) = 8.6 Calculate the square root of the right side: 2.93257566 Break this problem into two subproblems by setting (x + -1) equal to 2.93257566 and -2.93257566.Subproblem 1
x + -1 = 2.93257566 Simplifying x + -1 = 2.93257566 Reorder the terms: -1 + x = 2.93257566 Solving -1 + x = 2.93257566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.93257566 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.93257566 + 1 x = 2.93257566 + 1 Combine like terms: 2.93257566 + 1 = 3.93257566 x = 3.93257566 Simplifying x = 3.93257566Subproblem 2
x + -1 = -2.93257566 Simplifying x + -1 = -2.93257566 Reorder the terms: -1 + x = -2.93257566 Solving -1 + x = -2.93257566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.93257566 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.93257566 + 1 x = -2.93257566 + 1 Combine like terms: -2.93257566 + 1 = -1.93257566 x = -1.93257566 Simplifying x = -1.93257566Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.93257566, -1.93257566}Solution
x = {3.93257566, -1.93257566}
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