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Simplifying 39x2 + -278x + 410 = 0 Reorder the terms: 410 + -278x + 39x2 = 0 Solving 410 + -278x + 39x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. 10.51282051 + -7.128205128x + x2 = 0 Move the constant term to the right: Add '-10.51282051' to each side of the equation. 10.51282051 + -7.128205128x + -10.51282051 + x2 = 0 + -10.51282051 Reorder the terms: 10.51282051 + -10.51282051 + -7.128205128x + x2 = 0 + -10.51282051 Combine like terms: 10.51282051 + -10.51282051 = 0.00000000 0.00000000 + -7.128205128x + x2 = 0 + -10.51282051 -7.128205128x + x2 = 0 + -10.51282051 Combine like terms: 0 + -10.51282051 = -10.51282051 -7.128205128x + x2 = -10.51282051 The x term is -7.128205128x. Take half its coefficient (-3.564102564). Square it (12.70282709) and add it to both sides. Add '12.70282709' to each side of the equation. -7.128205128x + 12.70282709 + x2 = -10.51282051 + 12.70282709 Reorder the terms: 12.70282709 + -7.128205128x + x2 = -10.51282051 + 12.70282709 Combine like terms: -10.51282051 + 12.70282709 = 2.19000658 12.70282709 + -7.128205128x + x2 = 2.19000658 Factor a perfect square on the left side: (x + -3.564102564)(x + -3.564102564) = 2.19000658 Calculate the square root of the right side: 1.479867082 Break this problem into two subproblems by setting (x + -3.564102564) equal to 1.479867082 and -1.479867082.Subproblem 1
x + -3.564102564 = 1.479867082 Simplifying x + -3.564102564 = 1.479867082 Reorder the terms: -3.564102564 + x = 1.479867082 Solving -3.564102564 + x = 1.479867082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.564102564' to each side of the equation. -3.564102564 + 3.564102564 + x = 1.479867082 + 3.564102564 Combine like terms: -3.564102564 + 3.564102564 = 0.000000000 0.000000000 + x = 1.479867082 + 3.564102564 x = 1.479867082 + 3.564102564 Combine like terms: 1.479867082 + 3.564102564 = 5.043969646 x = 5.043969646 Simplifying x = 5.043969646Subproblem 2
x + -3.564102564 = -1.479867082 Simplifying x + -3.564102564 = -1.479867082 Reorder the terms: -3.564102564 + x = -1.479867082 Solving -3.564102564 + x = -1.479867082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.564102564' to each side of the equation. -3.564102564 + 3.564102564 + x = -1.479867082 + 3.564102564 Combine like terms: -3.564102564 + 3.564102564 = 0.000000000 0.000000000 + x = -1.479867082 + 3.564102564 x = -1.479867082 + 3.564102564 Combine like terms: -1.479867082 + 3.564102564 = 2.084235482 x = 2.084235482 Simplifying x = 2.084235482Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.043969646, 2.084235482}
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