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Simplifying 6x2 + 9x + -160 = 0 Reorder the terms: -160 + 9x + 6x2 = 0 Solving -160 + 9x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -26.66666667 + 1.5x + x2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + 1.5x + 26.66666667 + x2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + 1.5x + x2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + 1.5x + x2 = 0 + 26.66666667 1.5x + x2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 1.5x + x2 = 26.66666667 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 26.66666667 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 26.66666667 + 0.5625 Combine like terms: 26.66666667 + 0.5625 = 27.22916667 0.5625 + 1.5x + x2 = 27.22916667 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 27.22916667 Calculate the square root of the right side: 5.218157402 Break this problem into two subproblems by setting (x + 0.75) equal to 5.218157402 and -5.218157402.Subproblem 1
x + 0.75 = 5.218157402 Simplifying x + 0.75 = 5.218157402 Reorder the terms: 0.75 + x = 5.218157402 Solving 0.75 + x = 5.218157402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 5.218157402 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 5.218157402 + -0.75 x = 5.218157402 + -0.75 Combine like terms: 5.218157402 + -0.75 = 4.468157402 x = 4.468157402 Simplifying x = 4.468157402Subproblem 2
x + 0.75 = -5.218157402 Simplifying x + 0.75 = -5.218157402 Reorder the terms: 0.75 + x = -5.218157402 Solving 0.75 + x = -5.218157402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -5.218157402 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -5.218157402 + -0.75 x = -5.218157402 + -0.75 Combine like terms: -5.218157402 + -0.75 = -5.968157402 x = -5.968157402 Simplifying x = -5.968157402Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.468157402, -5.968157402}
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