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Simplifying 8.08x2 + 2.53x = 4.63 Reorder the terms: 2.53x + 8.08x2 = 4.63 Solving 2.53x + 8.08x2 = 4.63 Solving for variable 'x'. Reorder the terms: -4.63 + 2.53x + 8.08x2 = 4.63 + -4.63 Combine like terms: 4.63 + -4.63 = 0.00 -4.63 + 2.53x + 8.08x2 = 0.00 Begin completing the square. Divide all terms by 8.08 the coefficient of the squared term: Divide each side by '8.08'. -0.573019802 + 0.3131188119x + x2 = 0 Move the constant term to the right: Add '0.573019802' to each side of the equation. -0.573019802 + 0.3131188119x + 0.573019802 + x2 = 0 + 0.573019802 Reorder the terms: -0.573019802 + 0.573019802 + 0.3131188119x + x2 = 0 + 0.573019802 Combine like terms: -0.573019802 + 0.573019802 = 0.000000000 0.000000000 + 0.3131188119x + x2 = 0 + 0.573019802 0.3131188119x + x2 = 0 + 0.573019802 Combine like terms: 0 + 0.573019802 = 0.573019802 0.3131188119x + x2 = 0.573019802 The x term is 0.3131188119x. Take half its coefficient (0.156559406). Square it (0.02451084761) and add it to both sides. Add '0.02451084761' to each side of the equation. 0.3131188119x + 0.02451084761 + x2 = 0.573019802 + 0.02451084761 Reorder the terms: 0.02451084761 + 0.3131188119x + x2 = 0.573019802 + 0.02451084761 Combine like terms: 0.573019802 + 0.02451084761 = 0.59753064961 0.02451084761 + 0.3131188119x + x2 = 0.59753064961 Factor a perfect square on the left side: (x + 0.156559406)(x + 0.156559406) = 0.59753064961 Calculate the square root of the right side: 0.773001067 Break this problem into two subproblems by setting (x + 0.156559406) equal to 0.773001067 and -0.773001067.Subproblem 1
x + 0.156559406 = 0.773001067 Simplifying x + 0.156559406 = 0.773001067 Reorder the terms: 0.156559406 + x = 0.773001067 Solving 0.156559406 + x = 0.773001067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.156559406' to each side of the equation. 0.156559406 + -0.156559406 + x = 0.773001067 + -0.156559406 Combine like terms: 0.156559406 + -0.156559406 = 0.000000000 0.000000000 + x = 0.773001067 + -0.156559406 x = 0.773001067 + -0.156559406 Combine like terms: 0.773001067 + -0.156559406 = 0.616441661 x = 0.616441661 Simplifying x = 0.616441661Subproblem 2
x + 0.156559406 = -0.773001067 Simplifying x + 0.156559406 = -0.773001067 Reorder the terms: 0.156559406 + x = -0.773001067 Solving 0.156559406 + x = -0.773001067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.156559406' to each side of the equation. 0.156559406 + -0.156559406 + x = -0.773001067 + -0.156559406 Combine like terms: 0.156559406 + -0.156559406 = 0.000000000 0.000000000 + x = -0.773001067 + -0.156559406 x = -0.773001067 + -0.156559406 Combine like terms: -0.773001067 + -0.156559406 = -0.929560473 x = -0.929560473 Simplifying x = -0.929560473Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.616441661, -0.929560473}
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