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Simplifying (7 + 4x) = (5x)(10x) Remove parenthesis around (7 + 4x) 7 + 4x = (5x)(10x) Remove parenthesis around (5x) 7 + 4x = 5x(10x) Remove parenthesis around (10x) 7 + 4x = 5x * 10x Reorder the terms for easier multiplication: 7 + 4x = 5 * 10x * x Multiply 5 * 10 7 + 4x = 50x * x Multiply x * x 7 + 4x = 50x2 Solving 7 + 4x = 50x2 Solving for variable 'x'. Combine like terms: 50x2 + -50x2 = 0 7 + 4x + -50x2 = 0 Begin completing the square. Divide all terms by -50 the coefficient of the squared term: Divide each side by '-50'. -0.14 + -0.08x + x2 = 0 Move the constant term to the right: Add '0.14' to each side of the equation. -0.14 + -0.08x + 0.14 + x2 = 0 + 0.14 Reorder the terms: -0.14 + 0.14 + -0.08x + x2 = 0 + 0.14 Combine like terms: -0.14 + 0.14 = 0.00 0.00 + -0.08x + x2 = 0 + 0.14 -0.08x + x2 = 0 + 0.14 Combine like terms: 0 + 0.14 = 0.14 -0.08x + x2 = 0.14 The x term is -0.08x. Take half its coefficient (-0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. -0.08x + 0.0016 + x2 = 0.14 + 0.0016 Reorder the terms: 0.0016 + -0.08x + x2 = 0.14 + 0.0016 Combine like terms: 0.14 + 0.0016 = 0.1416 0.0016 + -0.08x + x2 = 0.1416 Factor a perfect square on the left side: (x + -0.04)(x + -0.04) = 0.1416 Calculate the square root of the right side: 0.376297754 Break this problem into two subproblems by setting (x + -0.04) equal to 0.376297754 and -0.376297754.Subproblem 1
x + -0.04 = 0.376297754 Simplifying x + -0.04 = 0.376297754 Reorder the terms: -0.04 + x = 0.376297754 Solving -0.04 + x = 0.376297754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + x = 0.376297754 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + x = 0.376297754 + 0.04 x = 0.376297754 + 0.04 Combine like terms: 0.376297754 + 0.04 = 0.416297754 x = 0.416297754 Simplifying x = 0.416297754Subproblem 2
x + -0.04 = -0.376297754 Simplifying x + -0.04 = -0.376297754 Reorder the terms: -0.04 + x = -0.376297754 Solving -0.04 + x = -0.376297754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + x = -0.376297754 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + x = -0.376297754 + 0.04 x = -0.376297754 + 0.04 Combine like terms: -0.376297754 + 0.04 = -0.336297754 x = -0.336297754 Simplifying x = -0.336297754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.416297754, -0.336297754}
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