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Simplifying 17x2 + x = 15 Reorder the terms: x + 17x2 = 15 Solving x + 17x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + x + 17x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.8823529412 + 0.05882352941x + x2 = 0 Move the constant term to the right: Add '0.8823529412' to each side of the equation. -0.8823529412 + 0.05882352941x + 0.8823529412 + x2 = 0 + 0.8823529412 Reorder the terms: -0.8823529412 + 0.8823529412 + 0.05882352941x + x2 = 0 + 0.8823529412 Combine like terms: -0.8823529412 + 0.8823529412 = 0.0000000000 0.0000000000 + 0.05882352941x + x2 = 0 + 0.8823529412 0.05882352941x + x2 = 0 + 0.8823529412 Combine like terms: 0 + 0.8823529412 = 0.8823529412 0.05882352941x + x2 = 0.8823529412 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.05882352941x + 0.25 + x2 = 0.8823529412 + 0.25 Reorder the terms: 0.25 + 0.05882352941x + x2 = 0.8823529412 + 0.25 Combine like terms: 0.8823529412 + 0.25 = 1.1323529412 0.25 + 0.05882352941x + x2 = 1.1323529412 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.1323529412 Calculate the square root of the right side: 1.064120736 Break this problem into two subproblems by setting (x + 0.5) equal to 1.064120736 and -1.064120736.Subproblem 1
x + 0.5 = 1.064120736 Simplifying x + 0.5 = 1.064120736 Reorder the terms: 0.5 + x = 1.064120736 Solving 0.5 + x = 1.064120736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.064120736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.064120736 + -0.5 x = 1.064120736 + -0.5 Combine like terms: 1.064120736 + -0.5 = 0.564120736 x = 0.564120736 Simplifying x = 0.564120736Subproblem 2
x + 0.5 = -1.064120736 Simplifying x + 0.5 = -1.064120736 Reorder the terms: 0.5 + x = -1.064120736 Solving 0.5 + x = -1.064120736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.064120736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.064120736 + -0.5 x = -1.064120736 + -0.5 Combine like terms: -1.064120736 + -0.5 = -1.564120736 x = -1.564120736 Simplifying x = -1.564120736Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.564120736, -1.564120736}
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