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Simplifying 0 = (0.84 + -1x)(0.75 + -1x) Multiply (0.84 + -1x) * (0.75 + -1x) 0 = (0.84(0.75 + -1x) + -1x * (0.75 + -1x)) 0 = ((0.75 * 0.84 + -1x * 0.84) + -1x * (0.75 + -1x)) 0 = ((0.63 + -0.84x) + -1x * (0.75 + -1x)) 0 = (0.63 + -0.84x + (0.75 * -1x + -1x * -1x)) 0 = (0.63 + -0.84x + (-0.75x + 1x2)) Combine like terms: -0.84x + -0.75x = -1.59x 0 = (0.63 + -1.59x + 1x2) Solving 0 = 0.63 + -1.59x + 1x2 Solving for variable 'x'. Combine like terms: 0 + -0.63 = -0.63 -0.63 + 1.59x + -1x2 = 0.63 + -1.59x + 1x2 + -0.63 + 1.59x + -1x2 Reorder the terms: -0.63 + 1.59x + -1x2 = 0.63 + -0.63 + -1.59x + 1.59x + 1x2 + -1x2 Combine like terms: 0.63 + -0.63 = 0.00 -0.63 + 1.59x + -1x2 = 0.00 + -1.59x + 1.59x + 1x2 + -1x2 -0.63 + 1.59x + -1x2 = -1.59x + 1.59x + 1x2 + -1x2 Combine like terms: -1.59x + 1.59x = 0.00 -0.63 + 1.59x + -1x2 = 0.00 + 1x2 + -1x2 -0.63 + 1.59x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -0.63 + 1.59x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.63 + -1.59x + x2 = 0 Move the constant term to the right: Add '-0.63' to each side of the equation. 0.63 + -1.59x + -0.63 + x2 = 0 + -0.63 Reorder the terms: 0.63 + -0.63 + -1.59x + x2 = 0 + -0.63 Combine like terms: 0.63 + -0.63 = 0.00 0.00 + -1.59x + x2 = 0 + -0.63 -1.59x + x2 = 0 + -0.63 Combine like terms: 0 + -0.63 = -0.63 -1.59x + x2 = -0.63 The x term is -1.59x. Take half its coefficient (-0.795). Square it (0.632025) and add it to both sides. Add '0.632025' to each side of the equation. -1.59x + 0.632025 + x2 = -0.63 + 0.632025 Reorder the terms: 0.632025 + -1.59x + x2 = -0.63 + 0.632025 Combine like terms: -0.63 + 0.632025 = 0.002025 0.632025 + -1.59x + x2 = 0.002025 Factor a perfect square on the left side: (x + -0.795)(x + -0.795) = 0.002025 Calculate the square root of the right side: 0.045 Break this problem into two subproblems by setting (x + -0.795) equal to 0.045 and -0.045.Subproblem 1
x + -0.795 = 0.045 Simplifying x + -0.795 = 0.045 Reorder the terms: -0.795 + x = 0.045 Solving -0.795 + x = 0.045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.795' to each side of the equation. -0.795 + 0.795 + x = 0.045 + 0.795 Combine like terms: -0.795 + 0.795 = 0.000 0.000 + x = 0.045 + 0.795 x = 0.045 + 0.795 Combine like terms: 0.045 + 0.795 = 0.84 x = 0.84 Simplifying x = 0.84Subproblem 2
x + -0.795 = -0.045 Simplifying x + -0.795 = -0.045 Reorder the terms: -0.795 + x = -0.045 Solving -0.795 + x = -0.045 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.795' to each side of the equation. -0.795 + 0.795 + x = -0.045 + 0.795 Combine like terms: -0.795 + 0.795 = 0.000 0.000 + x = -0.045 + 0.795 x = -0.045 + 0.795 Combine like terms: -0.045 + 0.795 = 0.75 x = 0.75 Simplifying x = 0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.84, 0.75}
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