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Simplifying 36x2 + 15x + -3 = 270 Reorder the terms: -3 + 15x + 36x2 = 270 Solving -3 + 15x + 36x2 = 270 Solving for variable 'x'. Reorder the terms: -3 + -270 + 15x + 36x2 = 270 + -270 Combine like terms: -3 + -270 = -273 -273 + 15x + 36x2 = 270 + -270 Combine like terms: 270 + -270 = 0 -273 + 15x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-91 + 5x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-91 + 5x + 12x2)' equal to zero and attempt to solve: Simplifying -91 + 5x + 12x2 = 0 Solving -91 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -7.583333333 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '7.583333333' to each side of the equation. -7.583333333 + 0.4166666667x + 7.583333333 + x2 = 0 + 7.583333333 Reorder the terms: -7.583333333 + 7.583333333 + 0.4166666667x + x2 = 0 + 7.583333333 Combine like terms: -7.583333333 + 7.583333333 = 0.000000000 0.000000000 + 0.4166666667x + x2 = 0 + 7.583333333 0.4166666667x + x2 = 0 + 7.583333333 Combine like terms: 0 + 7.583333333 = 7.583333333 0.4166666667x + x2 = 7.583333333 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 7.583333333 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 7.583333333 + 0.04340277781 Combine like terms: 7.583333333 + 0.04340277781 = 7.62673611081 0.04340277781 + 0.4166666667x + x2 = 7.62673611081 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 7.62673611081 Calculate the square root of the right side: 2.761654597 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 2.761654597 and -2.761654597.Subproblem 1
x + 0.2083333334 = 2.761654597 Simplifying x + 0.2083333334 = 2.761654597 Reorder the terms: 0.2083333334 + x = 2.761654597 Solving 0.2083333334 + x = 2.761654597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 2.761654597 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 2.761654597 + -0.2083333334 x = 2.761654597 + -0.2083333334 Combine like terms: 2.761654597 + -0.2083333334 = 2.5533212636 x = 2.5533212636 Simplifying x = 2.5533212636Subproblem 2
x + 0.2083333334 = -2.761654597 Simplifying x + 0.2083333334 = -2.761654597 Reorder the terms: 0.2083333334 + x = -2.761654597 Solving 0.2083333334 + x = -2.761654597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -2.761654597 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -2.761654597 + -0.2083333334 x = -2.761654597 + -0.2083333334 Combine like terms: -2.761654597 + -0.2083333334 = -2.9699879304 x = -2.9699879304 Simplifying x = -2.9699879304Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5533212636, -2.9699879304}Solution
x = {2.5533212636, -2.9699879304}
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