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Simplifying 8x2 + 7x = 36x + -9 Reorder the terms: 7x + 8x2 = 36x + -9 Reorder the terms: 7x + 8x2 = -9 + 36x Solving 7x + 8x2 = -9 + 36x Solving for variable 'x'. Reorder the terms: 9 + 7x + -36x + 8x2 = -9 + 36x + 9 + -36x Combine like terms: 7x + -36x = -29x 9 + -29x + 8x2 = -9 + 36x + 9 + -36x Reorder the terms: 9 + -29x + 8x2 = -9 + 9 + 36x + -36x Combine like terms: -9 + 9 = 0 9 + -29x + 8x2 = 0 + 36x + -36x 9 + -29x + 8x2 = 36x + -36x Combine like terms: 36x + -36x = 0 9 + -29x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -3.625x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -3.625x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -3.625x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -3.625x + x2 = 0 + -1.125 -3.625x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -3.625x + x2 = -1.125 The x term is -3.625x. Take half its coefficient (-1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. -3.625x + 3.28515625 + x2 = -1.125 + 3.28515625 Reorder the terms: 3.28515625 + -3.625x + x2 = -1.125 + 3.28515625 Combine like terms: -1.125 + 3.28515625 = 2.16015625 3.28515625 + -3.625x + x2 = 2.16015625 Factor a perfect square on the left side: (x + -1.8125)(x + -1.8125) = 2.16015625 Calculate the square root of the right side: 1.469747002 Break this problem into two subproblems by setting (x + -1.8125) equal to 1.469747002 and -1.469747002.Subproblem 1
x + -1.8125 = 1.469747002 Simplifying x + -1.8125 = 1.469747002 Reorder the terms: -1.8125 + x = 1.469747002 Solving -1.8125 + x = 1.469747002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = 1.469747002 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = 1.469747002 + 1.8125 x = 1.469747002 + 1.8125 Combine like terms: 1.469747002 + 1.8125 = 3.282247002 x = 3.282247002 Simplifying x = 3.282247002Subproblem 2
x + -1.8125 = -1.469747002 Simplifying x + -1.8125 = -1.469747002 Reorder the terms: -1.8125 + x = -1.469747002 Solving -1.8125 + x = -1.469747002 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = -1.469747002 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = -1.469747002 + 1.8125 x = -1.469747002 + 1.8125 Combine like terms: -1.469747002 + 1.8125 = 0.342752998 x = 0.342752998 Simplifying x = 0.342752998Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.282247002, 0.342752998}
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