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Simplifying (3.5 + -7x)(0.1x + 2.3) = 0 Reorder the terms: (3.5 + -7x)(2.3 + 0.1x) = 0 Multiply (3.5 + -7x) * (2.3 + 0.1x) (3.5(2.3 + 0.1x) + -7x * (2.3 + 0.1x)) = 0 ((2.3 * 3.5 + 0.1x * 3.5) + -7x * (2.3 + 0.1x)) = 0 ((8.05 + 0.35x) + -7x * (2.3 + 0.1x)) = 0 (8.05 + 0.35x + (2.3 * -7x + 0.1x * -7x)) = 0 (8.05 + 0.35x + (-16.1x + -0.7x2)) = 0 Combine like terms: 0.35x + -16.1x = -15.75x (8.05 + -15.75x + -0.7x2) = 0 Solving 8.05 + -15.75x + -0.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -11.5 + 22.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 22.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 22.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 22.5x + x2 = 0 + 11.5 22.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 22.5x + x2 = 11.5 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 11.5 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 11.5 + 126.5625 Combine like terms: 11.5 + 126.5625 = 138.0625 126.5625 + 22.5x + x2 = 138.0625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 138.0625 Calculate the square root of the right side: 11.75 Break this problem into two subproblems by setting (x + 11.25) equal to 11.75 and -11.75.Subproblem 1
x + 11.25 = 11.75 Simplifying x + 11.25 = 11.75 Reorder the terms: 11.25 + x = 11.75 Solving 11.25 + x = 11.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 11.75 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 11.75 + -11.25 x = 11.75 + -11.25 Combine like terms: 11.75 + -11.25 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 11.25 = -11.75 Simplifying x + 11.25 = -11.75 Reorder the terms: 11.25 + x = -11.75 Solving 11.25 + x = -11.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -11.75 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -11.75 + -11.25 x = -11.75 + -11.25 Combine like terms: -11.75 + -11.25 = -23 x = -23 Simplifying x = -23Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -23}
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