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Simplifying -2.2x + 4.9(-0.4x2 + 3x) = 8.18 Reorder the terms: -2.2x + 4.9(3x + -0.4x2) = 8.18 -2.2x + (3x * 4.9 + -0.4x2 * 4.9) = 8.18 -2.2x + (14.7x + -1.96x2) = 8.18 Combine like terms: -2.2x + 14.7x = 12.5x 12.5x + -1.96x2 = 8.18 Solving 12.5x + -1.96x2 = 8.18 Solving for variable 'x'. Reorder the terms: -8.18 + 12.5x + -1.96x2 = 8.18 + -8.18 Combine like terms: 8.18 + -8.18 = 0.00 -8.18 + 12.5x + -1.96x2 = 0.00 Begin completing the square. Divide all terms by -1.96 the coefficient of the squared term: Divide each side by '-1.96'. 4.173469388 + -6.37755102x + x2 = 0 Move the constant term to the right: Add '-4.173469388' to each side of the equation. 4.173469388 + -6.37755102x + -4.173469388 + x2 = 0 + -4.173469388 Reorder the terms: 4.173469388 + -4.173469388 + -6.37755102x + x2 = 0 + -4.173469388 Combine like terms: 4.173469388 + -4.173469388 = 0.000000000 0.000000000 + -6.37755102x + x2 = 0 + -4.173469388 -6.37755102x + x2 = 0 + -4.173469388 Combine like terms: 0 + -4.173469388 = -4.173469388 -6.37755102x + x2 = -4.173469388 The x term is -6.37755102x. Take half its coefficient (-3.18877551). Square it (10.16828925) and add it to both sides. Add '10.16828925' to each side of the equation. -6.37755102x + 10.16828925 + x2 = -4.173469388 + 10.16828925 Reorder the terms: 10.16828925 + -6.37755102x + x2 = -4.173469388 + 10.16828925 Combine like terms: -4.173469388 + 10.16828925 = 5.994819862 10.16828925 + -6.37755102x + x2 = 5.994819862 Factor a perfect square on the left side: (x + -3.18877551)(x + -3.18877551) = 5.994819862 Calculate the square root of the right side: 2.448432123 Break this problem into two subproblems by setting (x + -3.18877551) equal to 2.448432123 and -2.448432123.Subproblem 1
x + -3.18877551 = 2.448432123 Simplifying x + -3.18877551 = 2.448432123 Reorder the terms: -3.18877551 + x = 2.448432123 Solving -3.18877551 + x = 2.448432123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.18877551' to each side of the equation. -3.18877551 + 3.18877551 + x = 2.448432123 + 3.18877551 Combine like terms: -3.18877551 + 3.18877551 = 0.00000000 0.00000000 + x = 2.448432123 + 3.18877551 x = 2.448432123 + 3.18877551 Combine like terms: 2.448432123 + 3.18877551 = 5.637207633 x = 5.637207633 Simplifying x = 5.637207633Subproblem 2
x + -3.18877551 = -2.448432123 Simplifying x + -3.18877551 = -2.448432123 Reorder the terms: -3.18877551 + x = -2.448432123 Solving -3.18877551 + x = -2.448432123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.18877551' to each side of the equation. -3.18877551 + 3.18877551 + x = -2.448432123 + 3.18877551 Combine like terms: -3.18877551 + 3.18877551 = 0.00000000 0.00000000 + x = -2.448432123 + 3.18877551 x = -2.448432123 + 3.18877551 Combine like terms: -2.448432123 + 3.18877551 = 0.740343387 x = 0.740343387 Simplifying x = 0.740343387Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.637207633, 0.740343387}
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