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Simplifying 5x(2x + -14) + 23 = 7x + -14 Reorder the terms: 5x(-14 + 2x) + 23 = 7x + -14 (-14 * 5x + 2x * 5x) + 23 = 7x + -14 (-70x + 10x2) + 23 = 7x + -14 Reorder the terms: 23 + -70x + 10x2 = 7x + -14 Reorder the terms: 23 + -70x + 10x2 = -14 + 7x Solving 23 + -70x + 10x2 = -14 + 7x Solving for variable 'x'. Reorder the terms: 23 + 14 + -70x + -7x + 10x2 = -14 + 7x + 14 + -7x Combine like terms: 23 + 14 = 37 37 + -70x + -7x + 10x2 = -14 + 7x + 14 + -7x Combine like terms: -70x + -7x = -77x 37 + -77x + 10x2 = -14 + 7x + 14 + -7x Reorder the terms: 37 + -77x + 10x2 = -14 + 14 + 7x + -7x Combine like terms: -14 + 14 = 0 37 + -77x + 10x2 = 0 + 7x + -7x 37 + -77x + 10x2 = 7x + -7x Combine like terms: 7x + -7x = 0 37 + -77x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 3.7 + -7.7x + x2 = 0.0 Move the constant term to the right: Add '-3.7' to each side of the equation. 3.7 + -7.7x + -3.7 + x2 = 0.0 + -3.7 Reorder the terms: 3.7 + -3.7 + -7.7x + x2 = 0.0 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + -7.7x + x2 = 0.0 + -3.7 -7.7x + x2 = 0.0 + -3.7 Combine like terms: 0.0 + -3.7 = -3.7 -7.7x + x2 = -3.7 The x term is -7.7x. Take half its coefficient (-3.85). Square it (14.8225) and add it to both sides. Add '14.8225' to each side of the equation. -7.7x + 14.8225 + x2 = -3.7 + 14.8225 Reorder the terms: 14.8225 + -7.7x + x2 = -3.7 + 14.8225 Combine like terms: -3.7 + 14.8225 = 11.1225 14.8225 + -7.7x + x2 = 11.1225 Factor a perfect square on the left side: (x + -3.85)(x + -3.85) = 11.1225 Calculate the square root of the right side: 3.335041229 Break this problem into two subproblems by setting (x + -3.85) equal to 3.335041229 and -3.335041229.Subproblem 1
x + -3.85 = 3.335041229 Simplifying x + -3.85 = 3.335041229 Reorder the terms: -3.85 + x = 3.335041229 Solving -3.85 + x = 3.335041229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.85' to each side of the equation. -3.85 + 3.85 + x = 3.335041229 + 3.85 Combine like terms: -3.85 + 3.85 = 0.00 0.00 + x = 3.335041229 + 3.85 x = 3.335041229 + 3.85 Combine like terms: 3.335041229 + 3.85 = 7.185041229 x = 7.185041229 Simplifying x = 7.185041229Subproblem 2
x + -3.85 = -3.335041229 Simplifying x + -3.85 = -3.335041229 Reorder the terms: -3.85 + x = -3.335041229 Solving -3.85 + x = -3.335041229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.85' to each side of the equation. -3.85 + 3.85 + x = -3.335041229 + 3.85 Combine like terms: -3.85 + 3.85 = 0.00 0.00 + x = -3.335041229 + 3.85 x = -3.335041229 + 3.85 Combine like terms: -3.335041229 + 3.85 = 0.514958771 x = 0.514958771 Simplifying x = 0.514958771Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.185041229, 0.514958771}
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