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Simplifying (7x + 1)(9x + -7) = 90 Reorder the terms: (1 + 7x)(9x + -7) = 90 Reorder the terms: (1 + 7x)(-7 + 9x) = 90 Multiply (1 + 7x) * (-7 + 9x) (1(-7 + 9x) + 7x * (-7 + 9x)) = 90 ((-7 * 1 + 9x * 1) + 7x * (-7 + 9x)) = 90 ((-7 + 9x) + 7x * (-7 + 9x)) = 90 (-7 + 9x + (-7 * 7x + 9x * 7x)) = 90 (-7 + 9x + (-49x + 63x2)) = 90 Combine like terms: 9x + -49x = -40x (-7 + -40x + 63x2) = 90 Solving -7 + -40x + 63x2 = 90 Solving for variable 'x'. Reorder the terms: -7 + -90 + -40x + 63x2 = 90 + -90 Combine like terms: -7 + -90 = -97 -97 + -40x + 63x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -97 + -40x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -1.53968254 + -0.6349206349x + x2 = 0 Move the constant term to the right: Add '1.53968254' to each side of the equation. -1.53968254 + -0.6349206349x + 1.53968254 + x2 = 0 + 1.53968254 Reorder the terms: -1.53968254 + 1.53968254 + -0.6349206349x + x2 = 0 + 1.53968254 Combine like terms: -1.53968254 + 1.53968254 = 0.00000000 0.00000000 + -0.6349206349x + x2 = 0 + 1.53968254 -0.6349206349x + x2 = 0 + 1.53968254 Combine like terms: 0 + 1.53968254 = 1.53968254 -0.6349206349x + x2 = 1.53968254 The x term is -0.6349206349x. Take half its coefficient (-0.3174603175). Square it (0.1007810532) and add it to both sides. Add '0.1007810532' to each side of the equation. -0.6349206349x + 0.1007810532 + x2 = 1.53968254 + 0.1007810532 Reorder the terms: 0.1007810532 + -0.6349206349x + x2 = 1.53968254 + 0.1007810532 Combine like terms: 1.53968254 + 0.1007810532 = 1.6404635932 0.1007810532 + -0.6349206349x + x2 = 1.6404635932 Factor a perfect square on the left side: (x + -0.3174603175)(x + -0.3174603175) = 1.6404635932 Calculate the square root of the right side: 1.280805837 Break this problem into two subproblems by setting (x + -0.3174603175) equal to 1.280805837 and -1.280805837.Subproblem 1
x + -0.3174603175 = 1.280805837 Simplifying x + -0.3174603175 = 1.280805837 Reorder the terms: -0.3174603175 + x = 1.280805837 Solving -0.3174603175 + x = 1.280805837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3174603175' to each side of the equation. -0.3174603175 + 0.3174603175 + x = 1.280805837 + 0.3174603175 Combine like terms: -0.3174603175 + 0.3174603175 = 0.0000000000 0.0000000000 + x = 1.280805837 + 0.3174603175 x = 1.280805837 + 0.3174603175 Combine like terms: 1.280805837 + 0.3174603175 = 1.5982661545 x = 1.5982661545 Simplifying x = 1.5982661545Subproblem 2
x + -0.3174603175 = -1.280805837 Simplifying x + -0.3174603175 = -1.280805837 Reorder the terms: -0.3174603175 + x = -1.280805837 Solving -0.3174603175 + x = -1.280805837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3174603175' to each side of the equation. -0.3174603175 + 0.3174603175 + x = -1.280805837 + 0.3174603175 Combine like terms: -0.3174603175 + 0.3174603175 = 0.0000000000 0.0000000000 + x = -1.280805837 + 0.3174603175 x = -1.280805837 + 0.3174603175 Combine like terms: -1.280805837 + 0.3174603175 = -0.9633455195 x = -0.9633455195 Simplifying x = -0.9633455195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5982661545, -0.9633455195}
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