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Simplifying 6(3x + -5) * 7x = 25 Reorder the terms: 6(-5 + 3x) * 7x = 25 Reorder the terms for easier multiplication: 6 * 7x(-5 + 3x) = 25 Multiply 6 * 7 42x(-5 + 3x) = 25 (-5 * 42x + 3x * 42x) = 25 (-210x + 126x2) = 25 Solving -210x + 126x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -210x + 126x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -210x + 126x2 = 0 Begin completing the square. Divide all terms by 126 the coefficient of the squared term: Divide each side by '126'. -0.1984126984 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.1984126984' to each side of the equation. -0.1984126984 + -1.666666667x + 0.1984126984 + x2 = 0 + 0.1984126984 Reorder the terms: -0.1984126984 + 0.1984126984 + -1.666666667x + x2 = 0 + 0.1984126984 Combine like terms: -0.1984126984 + 0.1984126984 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + 0.1984126984 -1.666666667x + x2 = 0 + 0.1984126984 Combine like terms: 0 + 0.1984126984 = 0.1984126984 -1.666666667x + x2 = 0.1984126984 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 0.1984126984 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.1984126984 + 0.6944444447 Combine like terms: 0.1984126984 + 0.6944444447 = 0.8928571431 0.6944444447 + -1.666666667x + x2 = 0.8928571431 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.8928571431 Calculate the square root of the right side: 0.944911183 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.944911183 and -0.944911183.Subproblem 1
x + -0.8333333335 = 0.944911183 Simplifying x + -0.8333333335 = 0.944911183 Reorder the terms: -0.8333333335 + x = 0.944911183 Solving -0.8333333335 + x = 0.944911183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.944911183 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.944911183 + 0.8333333335 x = 0.944911183 + 0.8333333335 Combine like terms: 0.944911183 + 0.8333333335 = 1.7782445165 x = 1.7782445165 Simplifying x = 1.7782445165Subproblem 2
x + -0.8333333335 = -0.944911183 Simplifying x + -0.8333333335 = -0.944911183 Reorder the terms: -0.8333333335 + x = -0.944911183 Solving -0.8333333335 + x = -0.944911183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.944911183 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.944911183 + 0.8333333335 x = -0.944911183 + 0.8333333335 Combine like terms: -0.944911183 + 0.8333333335 = -0.1115778495 x = -0.1115778495 Simplifying x = -0.1115778495Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7782445165, -0.1115778495}
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