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Simplifying 5x2 + 17x + -6 = 0 Reorder the terms: -6 + 17x + 5x2 = 0 Solving -6 + 17x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 3.4x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 3.4x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 3.4x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 3.4x + x2 = 0 + 1.2 3.4x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 3.4x + x2 = 1.2 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = 1.2 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = 1.2 + 2.89 Combine like terms: 1.2 + 2.89 = 4.09 2.89 + 3.4x + x2 = 4.09 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + 1.7) equal to 2.022374842 and -2.022374842.Subproblem 1
x + 1.7 = 2.022374842 Simplifying x + 1.7 = 2.022374842 Reorder the terms: 1.7 + x = 2.022374842 Solving 1.7 + x = 2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 2.022374842 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 2.022374842 + -1.7 x = 2.022374842 + -1.7 Combine like terms: 2.022374842 + -1.7 = 0.322374842 x = 0.322374842 Simplifying x = 0.322374842Subproblem 2
x + 1.7 = -2.022374842 Simplifying x + 1.7 = -2.022374842 Reorder the terms: 1.7 + x = -2.022374842 Solving 1.7 + x = -2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -2.022374842 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -2.022374842 + -1.7 x = -2.022374842 + -1.7 Combine like terms: -2.022374842 + -1.7 = -3.722374842 x = -3.722374842 Simplifying x = -3.722374842Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.322374842, -3.722374842}
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