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Simplifying 30x2 + -36x + -15 = 0 Reorder the terms: -15 + -36x + 30x2 = 0 Solving -15 + -36x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -12x + 10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -12x + 10x2)' equal to zero and attempt to solve: Simplifying -5 + -12x + 10x2 = 0 Solving -5 + -12x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -1.2x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.2x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.2x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.2x + x2 = 0.0 + 0.5 -1.2x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -1.2x + x2 = 0.5 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 = 0.5 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.5 + 0.36 Combine like terms: 0.5 + 0.36 = 0.86 0.36 + -1.2x + x2 = 0.86 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.86 Calculate the square root of the right side: 0.92736185 Break this problem into two subproblems by setting (x + -0.6) equal to 0.92736185 and -0.92736185.Subproblem 1
x + -0.6 = 0.92736185 Simplifying x + -0.6 = 0.92736185 Reorder the terms: -0.6 + x = 0.92736185 Solving -0.6 + x = 0.92736185 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 = 0.92736185 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.92736185 + 0.6 x = 0.92736185 + 0.6 Combine like terms: 0.92736185 + 0.6 = 1.52736185 x = 1.52736185 Simplifying x = 1.52736185Subproblem 2
x + -0.6 = -0.92736185 Simplifying x + -0.6 = -0.92736185 Reorder the terms: -0.6 + x = -0.92736185 Solving -0.6 + x = -0.92736185 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 = -0.92736185 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.92736185 + 0.6 x = -0.92736185 + 0.6 Combine like terms: -0.92736185 + 0.6 = -0.32736185 x = -0.32736185 Simplifying x = -0.32736185Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.52736185, -0.32736185}Solution
x = {1.52736185, -0.32736185}
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