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Simplifying 0.0078x2 + 0.059x = 627.5 + -0.053 Reorder the terms: 0.059x + 0.0078x2 = 627.5 + -0.053 Combine like terms: 627.5 + -0.053 = 627.447 0.059x + 0.0078x2 = 627.447 Solving 0.059x + 0.0078x2 = 627.447 Solving for variable 'x'. Reorder the terms: -627.447 + 0.059x + 0.0078x2 = 627.447 + -627.447 Combine like terms: 627.447 + -627.447 = 0.000 -627.447 + 0.059x + 0.0078x2 = 0.000 Begin completing the square. Divide all terms by 0.0078 the coefficient of the squared term: Divide each side by '0.0078'. -80441.92308 + 7.564102564x + x2 = 0 Move the constant term to the right: Add '80441.92308' to each side of the equation. -80441.92308 + 7.564102564x + 80441.92308 + x2 = 0 + 80441.92308 Reorder the terms: -80441.92308 + 80441.92308 + 7.564102564x + x2 = 0 + 80441.92308 Combine like terms: -80441.92308 + 80441.92308 = 0.00000 0.00000 + 7.564102564x + x2 = 0 + 80441.92308 7.564102564x + x2 = 0 + 80441.92308 Combine like terms: 0 + 80441.92308 = 80441.92308 7.564102564x + x2 = 80441.92308 The x term is 7.564102564x. Take half its coefficient (3.782051282). Square it (14.30391190) and add it to both sides. Add '14.30391190' to each side of the equation. 7.564102564x + 14.30391190 + x2 = 80441.92308 + 14.30391190 Reorder the terms: 14.30391190 + 7.564102564x + x2 = 80441.92308 + 14.30391190 Combine like terms: 80441.92308 + 14.30391190 = 80456.2269919 14.30391190 + 7.564102564x + x2 = 80456.2269919 Factor a perfect square on the left side: (x + 3.782051282)(x + 3.782051282) = 80456.2269919 Calculate the square root of the right side: 283.648068902 Break this problem into two subproblems by setting (x + 3.782051282) equal to 283.648068902 and -283.648068902.Subproblem 1
x + 3.782051282 = 283.648068902 Simplifying x + 3.782051282 = 283.648068902 Reorder the terms: 3.782051282 + x = 283.648068902 Solving 3.782051282 + x = 283.648068902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.782051282' to each side of the equation. 3.782051282 + -3.782051282 + x = 283.648068902 + -3.782051282 Combine like terms: 3.782051282 + -3.782051282 = 0.000000000 0.000000000 + x = 283.648068902 + -3.782051282 x = 283.648068902 + -3.782051282 Combine like terms: 283.648068902 + -3.782051282 = 279.86601762 x = 279.86601762 Simplifying x = 279.86601762Subproblem 2
x + 3.782051282 = -283.648068902 Simplifying x + 3.782051282 = -283.648068902 Reorder the terms: 3.782051282 + x = -283.648068902 Solving 3.782051282 + x = -283.648068902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.782051282' to each side of the equation. 3.782051282 + -3.782051282 + x = -283.648068902 + -3.782051282 Combine like terms: 3.782051282 + -3.782051282 = 0.000000000 0.000000000 + x = -283.648068902 + -3.782051282 x = -283.648068902 + -3.782051282 Combine like terms: -283.648068902 + -3.782051282 = -287.430120184 x = -287.430120184 Simplifying x = -287.430120184Solution
The solution to the problem is based on the solutions from the subproblems. x = {279.86601762, -287.430120184}
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