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Simplifying 88x2 + -24x + -61 = 0 Reorder the terms: -61 + -24x + 88x2 = 0 Solving -61 + -24x + 88x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 88 the coefficient of the squared term: Divide each side by '88'. -0.6931818182 + -0.2727272727x + x2 = 0 Move the constant term to the right: Add '0.6931818182' to each side of the equation. -0.6931818182 + -0.2727272727x + 0.6931818182 + x2 = 0 + 0.6931818182 Reorder the terms: -0.6931818182 + 0.6931818182 + -0.2727272727x + x2 = 0 + 0.6931818182 Combine like terms: -0.6931818182 + 0.6931818182 = 0.0000000000 0.0000000000 + -0.2727272727x + x2 = 0 + 0.6931818182 -0.2727272727x + x2 = 0 + 0.6931818182 Combine like terms: 0 + 0.6931818182 = 0.6931818182 -0.2727272727x + x2 = 0.6931818182 The x term is -0.2727272727x. Take half its coefficient (-0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. -0.2727272727x + 0.01859504133 + x2 = 0.6931818182 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727x + x2 = 0.6931818182 + 0.01859504133 Combine like terms: 0.6931818182 + 0.01859504133 = 0.71177685953 0.01859504133 + -0.2727272727x + x2 = 0.71177685953 Factor a perfect square on the left side: (x + -0.1363636364)(x + -0.1363636364) = 0.71177685953 Calculate the square root of the right side: 0.843668691 Break this problem into two subproblems by setting (x + -0.1363636364) equal to 0.843668691 and -0.843668691.Subproblem 1
x + -0.1363636364 = 0.843668691 Simplifying x + -0.1363636364 = 0.843668691 Reorder the terms: -0.1363636364 + x = 0.843668691 Solving -0.1363636364 + x = 0.843668691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + x = 0.843668691 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = 0.843668691 + 0.1363636364 x = 0.843668691 + 0.1363636364 Combine like terms: 0.843668691 + 0.1363636364 = 0.9800323274 x = 0.9800323274 Simplifying x = 0.9800323274Subproblem 2
x + -0.1363636364 = -0.843668691 Simplifying x + -0.1363636364 = -0.843668691 Reorder the terms: -0.1363636364 + x = -0.843668691 Solving -0.1363636364 + x = -0.843668691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + x = -0.843668691 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = -0.843668691 + 0.1363636364 x = -0.843668691 + 0.1363636364 Combine like terms: -0.843668691 + 0.1363636364 = -0.7073050546 x = -0.7073050546 Simplifying x = -0.7073050546Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9800323274, -0.7073050546}
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