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Simplifying 0.7x(x + 90) + 0.9x = 127 Reorder the terms: 0.7x(90 + x) + 0.9x = 127 (90 * 0.7x + x * 0.7x) + 0.9x = 127 (63x + 0.7x2) + 0.9x = 127 Reorder the terms: 63x + 0.9x + 0.7x2 = 127 Combine like terms: 63x + 0.9x = 63.9x 63.9x + 0.7x2 = 127 Solving 63.9x + 0.7x2 = 127 Solving for variable 'x'. Reorder the terms: -127 + 63.9x + 0.7x2 = 127 + -127 Combine like terms: 127 + -127 = 0 -127 + 63.9x + 0.7x2 = 0 Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. -181.4285714 + 91.28571429x + x2 = 0 Move the constant term to the right: Add '181.4285714' to each side of the equation. -181.4285714 + 91.28571429x + 181.4285714 + x2 = 0 + 181.4285714 Reorder the terms: -181.4285714 + 181.4285714 + 91.28571429x + x2 = 0 + 181.4285714 Combine like terms: -181.4285714 + 181.4285714 = 0.0000000 0.0000000 + 91.28571429x + x2 = 0 + 181.4285714 91.28571429x + x2 = 0 + 181.4285714 Combine like terms: 0 + 181.4285714 = 181.4285714 91.28571429x + x2 = 181.4285714 The x term is 91.28571429x. Take half its coefficient (45.64285715). Square it (2083.270409) and add it to both sides. Add '2083.270409' to each side of the equation. 91.28571429x + 2083.270409 + x2 = 181.4285714 + 2083.270409 Reorder the terms: 2083.270409 + 91.28571429x + x2 = 181.4285714 + 2083.270409 Combine like terms: 181.4285714 + 2083.270409 = 2264.6989804 2083.270409 + 91.28571429x + x2 = 2264.6989804 Factor a perfect square on the left side: (x + 45.64285715)(x + 45.64285715) = 2264.6989804 Calculate the square root of the right side: 47.588853531 Break this problem into two subproblems by setting (x + 45.64285715) equal to 47.588853531 and -47.588853531.Subproblem 1
x + 45.64285715 = 47.588853531 Simplifying x + 45.64285715 = 47.588853531 Reorder the terms: 45.64285715 + x = 47.588853531 Solving 45.64285715 + x = 47.588853531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45.64285715' to each side of the equation. 45.64285715 + -45.64285715 + x = 47.588853531 + -45.64285715 Combine like terms: 45.64285715 + -45.64285715 = 0.00000000 0.00000000 + x = 47.588853531 + -45.64285715 x = 47.588853531 + -45.64285715 Combine like terms: 47.588853531 + -45.64285715 = 1.945996381 x = 1.945996381 Simplifying x = 1.945996381Subproblem 2
x + 45.64285715 = -47.588853531 Simplifying x + 45.64285715 = -47.588853531 Reorder the terms: 45.64285715 + x = -47.588853531 Solving 45.64285715 + x = -47.588853531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45.64285715' to each side of the equation. 45.64285715 + -45.64285715 + x = -47.588853531 + -45.64285715 Combine like terms: 45.64285715 + -45.64285715 = 0.00000000 0.00000000 + x = -47.588853531 + -45.64285715 x = -47.588853531 + -45.64285715 Combine like terms: -47.588853531 + -45.64285715 = -93.231710681 x = -93.231710681 Simplifying x = -93.231710681Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.945996381, -93.231710681}
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