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Simplifying 5(-3x2 + 36) + -3(-3x + 6) + 5 = 0 Reorder the terms: 5(36 + -3x2) + -3(-3x + 6) + 5 = 0 (36 * 5 + -3x2 * 5) + -3(-3x + 6) + 5 = 0 (180 + -15x2) + -3(-3x + 6) + 5 = 0 Reorder the terms: 180 + -15x2 + -3(6 + -3x) + 5 = 0 180 + -15x2 + (6 * -3 + -3x * -3) + 5 = 0 180 + -15x2 + (-18 + 9x) + 5 = 0 Reorder the terms: 180 + -18 + 5 + 9x + -15x2 = 0 Combine like terms: 180 + -18 = 162 162 + 5 + 9x + -15x2 = 0 Combine like terms: 162 + 5 = 167 167 + 9x + -15x2 = 0 Solving 167 + 9x + -15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -11.13333333 + -0.6x + x2 = 0 Move the constant term to the right: Add '11.13333333' to each side of the equation. -11.13333333 + -0.6x + 11.13333333 + x2 = 0 + 11.13333333 Reorder the terms: -11.13333333 + 11.13333333 + -0.6x + x2 = 0 + 11.13333333 Combine like terms: -11.13333333 + 11.13333333 = 0.00000000 0.00000000 + -0.6x + x2 = 0 + 11.13333333 -0.6x + x2 = 0 + 11.13333333 Combine like terms: 0 + 11.13333333 = 11.13333333 -0.6x + x2 = 11.13333333 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 11.13333333 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 11.13333333 + 0.09 Combine like terms: 11.13333333 + 0.09 = 11.22333333 0.09 + -0.6x + x2 = 11.22333333 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 11.22333333 Calculate the square root of the right side: 3.350124375 Break this problem into two subproblems by setting (x + -0.3) equal to 3.350124375 and -3.350124375.Subproblem 1
x + -0.3 = 3.350124375 Simplifying x + -0.3 = 3.350124375 Reorder the terms: -0.3 + x = 3.350124375 Solving -0.3 + x = 3.350124375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 3.350124375 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 3.350124375 + 0.3 x = 3.350124375 + 0.3 Combine like terms: 3.350124375 + 0.3 = 3.650124375 x = 3.650124375 Simplifying x = 3.650124375Subproblem 2
x + -0.3 = -3.350124375 Simplifying x + -0.3 = -3.350124375 Reorder the terms: -0.3 + x = -3.350124375 Solving -0.3 + x = -3.350124375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -3.350124375 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -3.350124375 + 0.3 x = -3.350124375 + 0.3 Combine like terms: -3.350124375 + 0.3 = -3.050124375 x = -3.050124375 Simplifying x = -3.050124375Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.650124375, -3.050124375}
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