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Simplifying 17x2 + 24x + -16 = 0 Reorder the terms: -16 + 24x + 17x2 = 0 Solving -16 + 24x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.9411764706 + 1.411764706x + x2 = 0 Move the constant term to the right: Add '0.9411764706' to each side of the equation. -0.9411764706 + 1.411764706x + 0.9411764706 + x2 = 0 + 0.9411764706 Reorder the terms: -0.9411764706 + 0.9411764706 + 1.411764706x + x2 = 0 + 0.9411764706 Combine like terms: -0.9411764706 + 0.9411764706 = 0.0000000000 0.0000000000 + 1.411764706x + x2 = 0 + 0.9411764706 1.411764706x + x2 = 0 + 0.9411764706 Combine like terms: 0 + 0.9411764706 = 0.9411764706 1.411764706x + x2 = 0.9411764706 The x term is 1.411764706x. Take half its coefficient (0.705882353). Square it (0.4982698963) and add it to both sides. Add '0.4982698963' to each side of the equation. 1.411764706x + 0.4982698963 + x2 = 0.9411764706 + 0.4982698963 Reorder the terms: 0.4982698963 + 1.411764706x + x2 = 0.9411764706 + 0.4982698963 Combine like terms: 0.9411764706 + 0.4982698963 = 1.4394463669 0.4982698963 + 1.411764706x + x2 = 1.4394463669 Factor a perfect square on the left side: (x + 0.705882353)(x + 0.705882353) = 1.4394463669 Calculate the square root of the right side: 1.199769297 Break this problem into two subproblems by setting (x + 0.705882353) equal to 1.199769297 and -1.199769297.Subproblem 1
x + 0.705882353 = 1.199769297 Simplifying x + 0.705882353 = 1.199769297 Reorder the terms: 0.705882353 + x = 1.199769297 Solving 0.705882353 + x = 1.199769297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.705882353' to each side of the equation. 0.705882353 + -0.705882353 + x = 1.199769297 + -0.705882353 Combine like terms: 0.705882353 + -0.705882353 = 0.000000000 0.000000000 + x = 1.199769297 + -0.705882353 x = 1.199769297 + -0.705882353 Combine like terms: 1.199769297 + -0.705882353 = 0.493886944 x = 0.493886944 Simplifying x = 0.493886944Subproblem 2
x + 0.705882353 = -1.199769297 Simplifying x + 0.705882353 = -1.199769297 Reorder the terms: 0.705882353 + x = -1.199769297 Solving 0.705882353 + x = -1.199769297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.705882353' to each side of the equation. 0.705882353 + -0.705882353 + x = -1.199769297 + -0.705882353 Combine like terms: 0.705882353 + -0.705882353 = 0.000000000 0.000000000 + x = -1.199769297 + -0.705882353 x = -1.199769297 + -0.705882353 Combine like terms: -1.199769297 + -0.705882353 = -1.90565165 x = -1.90565165 Simplifying x = -1.90565165Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.493886944, -1.90565165}
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