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Simplifying 6.2x2 + -14.63x + 7.26 = 0 Reorder the terms: 7.26 + -14.63x + 6.2x2 = 0 Solving 7.26 + -14.63x + 6.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.2 the coefficient of the squared term: Divide each side by '6.2'. 1.170967742 + -2.359677419x + x2 = 0 Move the constant term to the right: Add '-1.170967742' to each side of the equation. 1.170967742 + -2.359677419x + -1.170967742 + x2 = 0 + -1.170967742 Reorder the terms: 1.170967742 + -1.170967742 + -2.359677419x + x2 = 0 + -1.170967742 Combine like terms: 1.170967742 + -1.170967742 = 0.000000000 0.000000000 + -2.359677419x + x2 = 0 + -1.170967742 -2.359677419x + x2 = 0 + -1.170967742 Combine like terms: 0 + -1.170967742 = -1.170967742 -2.359677419x + x2 = -1.170967742 The x term is -2.359677419x. Take half its coefficient (-1.17983871). Square it (1.392019382) and add it to both sides. Add '1.392019382' to each side of the equation. -2.359677419x + 1.392019382 + x2 = -1.170967742 + 1.392019382 Reorder the terms: 1.392019382 + -2.359677419x + x2 = -1.170967742 + 1.392019382 Combine like terms: -1.170967742 + 1.392019382 = 0.22105164 1.392019382 + -2.359677419x + x2 = 0.22105164 Factor a perfect square on the left side: (x + -1.17983871)(x + -1.17983871) = 0.22105164 Calculate the square root of the right side: 0.470161291 Break this problem into two subproblems by setting (x + -1.17983871) equal to 0.470161291 and -0.470161291.Subproblem 1
x + -1.17983871 = 0.470161291 Simplifying x + -1.17983871 = 0.470161291 Reorder the terms: -1.17983871 + x = 0.470161291 Solving -1.17983871 + x = 0.470161291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.17983871' to each side of the equation. -1.17983871 + 1.17983871 + x = 0.470161291 + 1.17983871 Combine like terms: -1.17983871 + 1.17983871 = 0.00000000 0.00000000 + x = 0.470161291 + 1.17983871 x = 0.470161291 + 1.17983871 Combine like terms: 0.470161291 + 1.17983871 = 1.650000001 x = 1.650000001 Simplifying x = 1.650000001Subproblem 2
x + -1.17983871 = -0.470161291 Simplifying x + -1.17983871 = -0.470161291 Reorder the terms: -1.17983871 + x = -0.470161291 Solving -1.17983871 + x = -0.470161291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.17983871' to each side of the equation. -1.17983871 + 1.17983871 + x = -0.470161291 + 1.17983871 Combine like terms: -1.17983871 + 1.17983871 = 0.00000000 0.00000000 + x = -0.470161291 + 1.17983871 x = -0.470161291 + 1.17983871 Combine like terms: -0.470161291 + 1.17983871 = 0.709677419 x = 0.709677419 Simplifying x = 0.709677419Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.650000001, 0.709677419}
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