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Simplifying 320x2 + 5x + -6 = 6x2 + -12x Reorder the terms: -6 + 5x + 320x2 = 6x2 + -12x Reorder the terms: -6 + 5x + 320x2 = -12x + 6x2 Solving -6 + 5x + 320x2 = -12x + 6x2 Solving for variable 'x'. Reorder the terms: -6 + 5x + 12x + 320x2 + -6x2 = -12x + 6x2 + 12x + -6x2 Combine like terms: 5x + 12x = 17x -6 + 17x + 320x2 + -6x2 = -12x + 6x2 + 12x + -6x2 Combine like terms: 320x2 + -6x2 = 314x2 -6 + 17x + 314x2 = -12x + 6x2 + 12x + -6x2 Reorder the terms: -6 + 17x + 314x2 = -12x + 12x + 6x2 + -6x2 Combine like terms: -12x + 12x = 0 -6 + 17x + 314x2 = 0 + 6x2 + -6x2 -6 + 17x + 314x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -6 + 17x + 314x2 = 0 Begin completing the square. Divide all terms by 314 the coefficient of the squared term: Divide each side by '314'. -0.01910828025 + 0.05414012739x + x2 = 0 Move the constant term to the right: Add '0.01910828025' to each side of the equation. -0.01910828025 + 0.05414012739x + 0.01910828025 + x2 = 0 + 0.01910828025 Reorder the terms: -0.01910828025 + 0.01910828025 + 0.05414012739x + x2 = 0 + 0.01910828025 Combine like terms: -0.01910828025 + 0.01910828025 = 0.00000000000 0.00000000000 + 0.05414012739x + x2 = 0 + 0.01910828025 0.05414012739x + x2 = 0 + 0.01910828025 Combine like terms: 0 + 0.01910828025 = 0.01910828025 0.05414012739x + x2 = 0.01910828025 The x term is 0.05414012739x. Take half its coefficient (0.0270700637). Square it (0.0007327883487) and add it to both sides. Add '0.0007327883487' to each side of the equation. 0.05414012739x + 0.0007327883487 + x2 = 0.01910828025 + 0.0007327883487 Reorder the terms: 0.0007327883487 + 0.05414012739x + x2 = 0.01910828025 + 0.0007327883487 Combine like terms: 0.01910828025 + 0.0007327883487 = 0.0198410685987 0.0007327883487 + 0.05414012739x + x2 = 0.0198410685987 Factor a perfect square on the left side: (x + 0.0270700637)(x + 0.0270700637) = 0.0198410685987 Calculate the square root of the right side: 0.140858328 Break this problem into two subproblems by setting (x + 0.0270700637) equal to 0.140858328 and -0.140858328.Subproblem 1
x + 0.0270700637 = 0.140858328 Simplifying x + 0.0270700637 = 0.140858328 Reorder the terms: 0.0270700637 + x = 0.140858328 Solving 0.0270700637 + x = 0.140858328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0270700637' to each side of the equation. 0.0270700637 + -0.0270700637 + x = 0.140858328 + -0.0270700637 Combine like terms: 0.0270700637 + -0.0270700637 = 0.0000000000 0.0000000000 + x = 0.140858328 + -0.0270700637 x = 0.140858328 + -0.0270700637 Combine like terms: 0.140858328 + -0.0270700637 = 0.1137882643 x = 0.1137882643 Simplifying x = 0.1137882643Subproblem 2
x + 0.0270700637 = -0.140858328 Simplifying x + 0.0270700637 = -0.140858328 Reorder the terms: 0.0270700637 + x = -0.140858328 Solving 0.0270700637 + x = -0.140858328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0270700637' to each side of the equation. 0.0270700637 + -0.0270700637 + x = -0.140858328 + -0.0270700637 Combine like terms: 0.0270700637 + -0.0270700637 = 0.0000000000 0.0000000000 + x = -0.140858328 + -0.0270700637 x = -0.140858328 + -0.0270700637 Combine like terms: -0.140858328 + -0.0270700637 = -0.1679283917 x = -0.1679283917 Simplifying x = -0.1679283917Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1137882643, -0.1679283917}
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