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Simplifying 3 + -10x(6 + -5x) = 7x + -16 3 + (6 * -10x + -5x * -10x) = 7x + -16 3 + (-60x + 50x2) = 7x + -16 Reorder the terms: 3 + -60x + 50x2 = -16 + 7x Solving 3 + -60x + 50x2 = -16 + 7x Solving for variable 'x'. Reorder the terms: 3 + 16 + -60x + -7x + 50x2 = -16 + 7x + 16 + -7x Combine like terms: 3 + 16 = 19 19 + -60x + -7x + 50x2 = -16 + 7x + 16 + -7x Combine like terms: -60x + -7x = -67x 19 + -67x + 50x2 = -16 + 7x + 16 + -7x Reorder the terms: 19 + -67x + 50x2 = -16 + 16 + 7x + -7x Combine like terms: -16 + 16 = 0 19 + -67x + 50x2 = 0 + 7x + -7x 19 + -67x + 50x2 = 7x + -7x Combine like terms: 7x + -7x = 0 19 + -67x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.38 + -1.34x + x2 = 0.0 Move the constant term to the right: Add '-0.38' to each side of the equation. 0.38 + -1.34x + -0.38 + x2 = 0.0 + -0.38 Reorder the terms: 0.38 + -0.38 + -1.34x + x2 = 0.0 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + -1.34x + x2 = 0.0 + -0.38 -1.34x + x2 = 0.0 + -0.38 Combine like terms: 0.0 + -0.38 = -0.38 -1.34x + x2 = -0.38 The x term is -1.34x. Take half its coefficient (-0.67). Square it (0.4489) and add it to both sides. Add '0.4489' to each side of the equation. -1.34x + 0.4489 + x2 = -0.38 + 0.4489 Reorder the terms: 0.4489 + -1.34x + x2 = -0.38 + 0.4489 Combine like terms: -0.38 + 0.4489 = 0.0689 0.4489 + -1.34x + x2 = 0.0689 Factor a perfect square on the left side: (x + -0.67)(x + -0.67) = 0.0689 Calculate the square root of the right side: 0.262488095 Break this problem into two subproblems by setting (x + -0.67) equal to 0.262488095 and -0.262488095.Subproblem 1
x + -0.67 = 0.262488095 Simplifying x + -0.67 = 0.262488095 Reorder the terms: -0.67 + x = 0.262488095 Solving -0.67 + x = 0.262488095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.67' to each side of the equation. -0.67 + 0.67 + x = 0.262488095 + 0.67 Combine like terms: -0.67 + 0.67 = 0.00 0.00 + x = 0.262488095 + 0.67 x = 0.262488095 + 0.67 Combine like terms: 0.262488095 + 0.67 = 0.932488095 x = 0.932488095 Simplifying x = 0.932488095Subproblem 2
x + -0.67 = -0.262488095 Simplifying x + -0.67 = -0.262488095 Reorder the terms: -0.67 + x = -0.262488095 Solving -0.67 + x = -0.262488095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.67' to each side of the equation. -0.67 + 0.67 + x = -0.262488095 + 0.67 Combine like terms: -0.67 + 0.67 = 0.00 0.00 + x = -0.262488095 + 0.67 x = -0.262488095 + 0.67 Combine like terms: -0.262488095 + 0.67 = 0.407511905 x = 0.407511905 Simplifying x = 0.407511905Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.932488095, 0.407511905}
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