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Simplifying -28.3 = 5.16x + -4.9x2 Solving -28.3 = 5.16x + -4.9x2 Solving for variable 'x'. Reorder the terms: -28.3 + -5.16x + 4.9x2 = 5.16x + -5.16x + -4.9x2 + 4.9x2 Combine like terms: 5.16x + -5.16x = 0.00 -28.3 + -5.16x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 -28.3 + -5.16x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -28.3 + -5.16x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -5.775510204 + -1.053061224x + x2 = 0 Move the constant term to the right: Add '5.775510204' to each side of the equation. -5.775510204 + -1.053061224x + 5.775510204 + x2 = 0 + 5.775510204 Reorder the terms: -5.775510204 + 5.775510204 + -1.053061224x + x2 = 0 + 5.775510204 Combine like terms: -5.775510204 + 5.775510204 = 0.000000000 0.000000000 + -1.053061224x + x2 = 0 + 5.775510204 -1.053061224x + x2 = 0 + 5.775510204 Combine like terms: 0 + 5.775510204 = 5.775510204 -1.053061224x + x2 = 5.775510204 The x term is -1.053061224x. Take half its coefficient (-0.526530612). Square it (0.2772344854) and add it to both sides. Add '0.2772344854' to each side of the equation. -1.053061224x + 0.2772344854 + x2 = 5.775510204 + 0.2772344854 Reorder the terms: 0.2772344854 + -1.053061224x + x2 = 5.775510204 + 0.2772344854 Combine like terms: 5.775510204 + 0.2772344854 = 6.0527446894 0.2772344854 + -1.053061224x + x2 = 6.0527446894 Factor a perfect square on the left side: (x + -0.526530612)(x + -0.526530612) = 6.0527446894 Calculate the square root of the right side: 2.460232649 Break this problem into two subproblems by setting (x + -0.526530612) equal to 2.460232649 and -2.460232649.Subproblem 1
x + -0.526530612 = 2.460232649 Simplifying x + -0.526530612 = 2.460232649 Reorder the terms: -0.526530612 + x = 2.460232649 Solving -0.526530612 + x = 2.460232649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.526530612' to each side of the equation. -0.526530612 + 0.526530612 + x = 2.460232649 + 0.526530612 Combine like terms: -0.526530612 + 0.526530612 = 0.000000000 0.000000000 + x = 2.460232649 + 0.526530612 x = 2.460232649 + 0.526530612 Combine like terms: 2.460232649 + 0.526530612 = 2.986763261 x = 2.986763261 Simplifying x = 2.986763261Subproblem 2
x + -0.526530612 = -2.460232649 Simplifying x + -0.526530612 = -2.460232649 Reorder the terms: -0.526530612 + x = -2.460232649 Solving -0.526530612 + x = -2.460232649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.526530612' to each side of the equation. -0.526530612 + 0.526530612 + x = -2.460232649 + 0.526530612 Combine like terms: -0.526530612 + 0.526530612 = 0.000000000 0.000000000 + x = -2.460232649 + 0.526530612 x = -2.460232649 + 0.526530612 Combine like terms: -2.460232649 + 0.526530612 = -1.933702037 x = -1.933702037 Simplifying x = -1.933702037Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.986763261, -1.933702037}
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