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Simplifying (9x2 + -90x + -8) + (8x2 + -4) = 0 Reorder the terms: (-8 + -90x + 9x2) + (8x2 + -4) = 0 Remove parenthesis around (-8 + -90x + 9x2) -8 + -90x + 9x2 + (8x2 + -4) = 0 Reorder the terms: -8 + -90x + 9x2 + (-4 + 8x2) = 0 Remove parenthesis around (-4 + 8x2) -8 + -90x + 9x2 + -4 + 8x2 = 0 Reorder the terms: -8 + -4 + -90x + 9x2 + 8x2 = 0 Combine like terms: -8 + -4 = -12 -12 + -90x + 9x2 + 8x2 = 0 Combine like terms: 9x2 + 8x2 = 17x2 -12 + -90x + 17x2 = 0 Solving -12 + -90x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.7058823529 + -5.294117647x + x2 = 0 Move the constant term to the right: Add '0.7058823529' to each side of the equation. -0.7058823529 + -5.294117647x + 0.7058823529 + x2 = 0 + 0.7058823529 Reorder the terms: -0.7058823529 + 0.7058823529 + -5.294117647x + x2 = 0 + 0.7058823529 Combine like terms: -0.7058823529 + 0.7058823529 = 0.0000000000 0.0000000000 + -5.294117647x + x2 = 0 + 0.7058823529 -5.294117647x + x2 = 0 + 0.7058823529 Combine like terms: 0 + 0.7058823529 = 0.7058823529 -5.294117647x + x2 = 0.7058823529 The x term is -5.294117647x. Take half its coefficient (-2.647058824). Square it (7.006920418) and add it to both sides. Add '7.006920418' to each side of the equation. -5.294117647x + 7.006920418 + x2 = 0.7058823529 + 7.006920418 Reorder the terms: 7.006920418 + -5.294117647x + x2 = 0.7058823529 + 7.006920418 Combine like terms: 0.7058823529 + 7.006920418 = 7.7128027709 7.006920418 + -5.294117647x + x2 = 7.7128027709 Factor a perfect square on the left side: (x + -2.647058824)(x + -2.647058824) = 7.7128027709 Calculate the square root of the right side: 2.777193326 Break this problem into two subproblems by setting (x + -2.647058824) equal to 2.777193326 and -2.777193326.Subproblem 1
x + -2.647058824 = 2.777193326 Simplifying x + -2.647058824 = 2.777193326 Reorder the terms: -2.647058824 + x = 2.777193326 Solving -2.647058824 + x = 2.777193326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.647058824' to each side of the equation. -2.647058824 + 2.647058824 + x = 2.777193326 + 2.647058824 Combine like terms: -2.647058824 + 2.647058824 = 0.000000000 0.000000000 + x = 2.777193326 + 2.647058824 x = 2.777193326 + 2.647058824 Combine like terms: 2.777193326 + 2.647058824 = 5.42425215 x = 5.42425215 Simplifying x = 5.42425215Subproblem 2
x + -2.647058824 = -2.777193326 Simplifying x + -2.647058824 = -2.777193326 Reorder the terms: -2.647058824 + x = -2.777193326 Solving -2.647058824 + x = -2.777193326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.647058824' to each side of the equation. -2.647058824 + 2.647058824 + x = -2.777193326 + 2.647058824 Combine like terms: -2.647058824 + 2.647058824 = 0.000000000 0.000000000 + x = -2.777193326 + 2.647058824 x = -2.777193326 + 2.647058824 Combine like terms: -2.777193326 + 2.647058824 = -0.130134502 x = -0.130134502 Simplifying x = -0.130134502Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.42425215, -0.130134502}
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