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Simplifying (8x2 + -2x + 25) + (7x2 + 9x + -86) = 0 Reorder the terms: (25 + -2x + 8x2) + (7x2 + 9x + -86) = 0 Remove parenthesis around (25 + -2x + 8x2) 25 + -2x + 8x2 + (7x2 + 9x + -86) = 0 Reorder the terms: 25 + -2x + 8x2 + (-86 + 9x + 7x2) = 0 Remove parenthesis around (-86 + 9x + 7x2) 25 + -2x + 8x2 + -86 + 9x + 7x2 = 0 Reorder the terms: 25 + -86 + -2x + 9x + 8x2 + 7x2 = 0 Combine like terms: 25 + -86 = -61 -61 + -2x + 9x + 8x2 + 7x2 = 0 Combine like terms: -2x + 9x = 7x -61 + 7x + 8x2 + 7x2 = 0 Combine like terms: 8x2 + 7x2 = 15x2 -61 + 7x + 15x2 = 0 Solving -61 + 7x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4.066666667 + 0.4666666667x + x2 = 0 Move the constant term to the right: Add '4.066666667' to each side of the equation. -4.066666667 + 0.4666666667x + 4.066666667 + x2 = 0 + 4.066666667 Reorder the terms: -4.066666667 + 4.066666667 + 0.4666666667x + x2 = 0 + 4.066666667 Combine like terms: -4.066666667 + 4.066666667 = 0.000000000 0.000000000 + 0.4666666667x + x2 = 0 + 4.066666667 0.4666666667x + x2 = 0 + 4.066666667 Combine like terms: 0 + 4.066666667 = 4.066666667 0.4666666667x + x2 = 4.066666667 The x term is 0.4666666667x. Take half its coefficient (0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. 0.4666666667x + 0.05444444448 + x2 = 4.066666667 + 0.05444444448 Reorder the terms: 0.05444444448 + 0.4666666667x + x2 = 4.066666667 + 0.05444444448 Combine like terms: 4.066666667 + 0.05444444448 = 4.12111111148 0.05444444448 + 0.4666666667x + x2 = 4.12111111148 Factor a perfect square on the left side: (x + 0.2333333334)(x + 0.2333333334) = 4.12111111148 Calculate the square root of the right side: 2.030051997 Break this problem into two subproblems by setting (x + 0.2333333334) equal to 2.030051997 and -2.030051997.Subproblem 1
x + 0.2333333334 = 2.030051997 Simplifying x + 0.2333333334 = 2.030051997 Reorder the terms: 0.2333333334 + x = 2.030051997 Solving 0.2333333334 + x = 2.030051997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2333333334' to each side of the equation. 0.2333333334 + -0.2333333334 + x = 2.030051997 + -0.2333333334 Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000 0.0000000000 + x = 2.030051997 + -0.2333333334 x = 2.030051997 + -0.2333333334 Combine like terms: 2.030051997 + -0.2333333334 = 1.7967186636 x = 1.7967186636 Simplifying x = 1.7967186636Subproblem 2
x + 0.2333333334 = -2.030051997 Simplifying x + 0.2333333334 = -2.030051997 Reorder the terms: 0.2333333334 + x = -2.030051997 Solving 0.2333333334 + x = -2.030051997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2333333334' to each side of the equation. 0.2333333334 + -0.2333333334 + x = -2.030051997 + -0.2333333334 Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000 0.0000000000 + x = -2.030051997 + -0.2333333334 x = -2.030051997 + -0.2333333334 Combine like terms: -2.030051997 + -0.2333333334 = -2.2633853304 x = -2.2633853304 Simplifying x = -2.2633853304Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7967186636, -2.2633853304}
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