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Simplifying 7.65x2 + 2.72x = 5.31 Reorder the terms: 2.72x + 7.65x2 = 5.31 Solving 2.72x + 7.65x2 = 5.31 Solving for variable 'x'. Reorder the terms: -5.31 + 2.72x + 7.65x2 = 5.31 + -5.31 Combine like terms: 5.31 + -5.31 = 0.00 -5.31 + 2.72x + 7.65x2 = 0.00 Begin completing the square. Divide all terms by 7.65 the coefficient of the squared term: Divide each side by '7.65'. -0.6941176471 + 0.3555555556x + x2 = 0 Move the constant term to the right: Add '0.6941176471' to each side of the equation. -0.6941176471 + 0.3555555556x + 0.6941176471 + x2 = 0 + 0.6941176471 Reorder the terms: -0.6941176471 + 0.6941176471 + 0.3555555556x + x2 = 0 + 0.6941176471 Combine like terms: -0.6941176471 + 0.6941176471 = 0.0000000000 0.0000000000 + 0.3555555556x + x2 = 0 + 0.6941176471 0.3555555556x + x2 = 0 + 0.6941176471 Combine like terms: 0 + 0.6941176471 = 0.6941176471 0.3555555556x + x2 = 0.6941176471 The x term is 0.3555555556x. Take half its coefficient (0.1777777778). Square it (0.03160493828) and add it to both sides. Add '0.03160493828' to each side of the equation. 0.3555555556x + 0.03160493828 + x2 = 0.6941176471 + 0.03160493828 Reorder the terms: 0.03160493828 + 0.3555555556x + x2 = 0.6941176471 + 0.03160493828 Combine like terms: 0.6941176471 + 0.03160493828 = 0.72572258538 0.03160493828 + 0.3555555556x + x2 = 0.72572258538 Factor a perfect square on the left side: (x + 0.1777777778)(x + 0.1777777778) = 0.72572258538 Calculate the square root of the right side: 0.851893529 Break this problem into two subproblems by setting (x + 0.1777777778) equal to 0.851893529 and -0.851893529.Subproblem 1
x + 0.1777777778 = 0.851893529 Simplifying x + 0.1777777778 = 0.851893529 Reorder the terms: 0.1777777778 + x = 0.851893529 Solving 0.1777777778 + x = 0.851893529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1777777778' to each side of the equation. 0.1777777778 + -0.1777777778 + x = 0.851893529 + -0.1777777778 Combine like terms: 0.1777777778 + -0.1777777778 = 0.0000000000 0.0000000000 + x = 0.851893529 + -0.1777777778 x = 0.851893529 + -0.1777777778 Combine like terms: 0.851893529 + -0.1777777778 = 0.6741157512 x = 0.6741157512 Simplifying x = 0.6741157512Subproblem 2
x + 0.1777777778 = -0.851893529 Simplifying x + 0.1777777778 = -0.851893529 Reorder the terms: 0.1777777778 + x = -0.851893529 Solving 0.1777777778 + x = -0.851893529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1777777778' to each side of the equation. 0.1777777778 + -0.1777777778 + x = -0.851893529 + -0.1777777778 Combine like terms: 0.1777777778 + -0.1777777778 = 0.0000000000 0.0000000000 + x = -0.851893529 + -0.1777777778 x = -0.851893529 + -0.1777777778 Combine like terms: -0.851893529 + -0.1777777778 = -1.0296713068 x = -1.0296713068 Simplifying x = -1.0296713068Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6741157512, -1.0296713068}
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