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Simplifying 0.17 = 2x + x2 Solving 0.17 = 2x + x2 Solving for variable 'x'. Reorder the terms: 0.17 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 0.17 + -2x + -1x2 = 0 + x2 + -1x2 0.17 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.17 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.17 + 2x + x2 = 0 Move the constant term to the right: Add '0.17' to each side of the equation. -0.17 + 2x + 0.17 + x2 = 0 + 0.17 Reorder the terms: -0.17 + 0.17 + 2x + x2 = 0 + 0.17 Combine like terms: -0.17 + 0.17 = 0.00 0.00 + 2x + x2 = 0 + 0.17 2x + x2 = 0 + 0.17 Combine like terms: 0 + 0.17 = 0.17 2x + x2 = 0.17 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.17 + 1 Reorder the terms: 1 + 2x + x2 = 0.17 + 1 Combine like terms: 0.17 + 1 = 1.17 1 + 2x + x2 = 1.17 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.17 Calculate the square root of the right side: 1.081665383 Break this problem into two subproblems by setting (x + 1) equal to 1.081665383 and -1.081665383.Subproblem 1
x + 1 = 1.081665383 Simplifying x + 1 = 1.081665383 Reorder the terms: 1 + x = 1.081665383 Solving 1 + x = 1.081665383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.081665383 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.081665383 + -1 x = 1.081665383 + -1 Combine like terms: 1.081665383 + -1 = 0.081665383 x = 0.081665383 Simplifying x = 0.081665383Subproblem 2
x + 1 = -1.081665383 Simplifying x + 1 = -1.081665383 Reorder the terms: 1 + x = -1.081665383 Solving 1 + x = -1.081665383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.081665383 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.081665383 + -1 x = -1.081665383 + -1 Combine like terms: -1.081665383 + -1 = -2.081665383 x = -2.081665383 Simplifying x = -2.081665383Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.081665383, -2.081665383}
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