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Simplifying 17x2 + 48x + -14 = 0 Reorder the terms: -14 + 48x + 17x2 = 0 Solving -14 + 48x + 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'. -0.8235294118 + 2.823529412x + x2 = 0 Move the constant term to the right: Add '0.8235294118' to each side of the equation. -0.8235294118 + 2.823529412x + 0.8235294118 + x2 = 0 + 0.8235294118 Reorder the terms: -0.8235294118 + 0.8235294118 + 2.823529412x + x2 = 0 + 0.8235294118 Combine like terms: -0.8235294118 + 0.8235294118 = 0.0000000000 0.0000000000 + 2.823529412x + x2 = 0 + 0.8235294118 2.823529412x + x2 = 0 + 0.8235294118 Combine like terms: 0 + 0.8235294118 = 0.8235294118 2.823529412x + x2 = 0.8235294118 The x term is 2.823529412x. Take half its coefficient (1.411764706). Square it (1.993079585) and add it to both sides. Add '1.993079585' to each side of the equation. 2.823529412x + 1.993079585 + x2 = 0.8235294118 + 1.993079585 Reorder the terms: 1.993079585 + 2.823529412x + x2 = 0.8235294118 + 1.993079585 Combine like terms: 0.8235294118 + 1.993079585 = 2.8166089968 1.993079585 + 2.823529412x + x2 = 2.8166089968 Factor a perfect square on the left side: (x + 1.411764706)(x + 1.411764706) = 2.8166089968 Calculate the square root of the right side: 1.678275602 Break this problem into two subproblems by setting (x + 1.411764706) equal to 1.678275602 and -1.678275602.Subproblem 1
x + 1.411764706 = 1.678275602 Simplifying x + 1.411764706 = 1.678275602 Reorder the terms: 1.411764706 + x = 1.678275602 Solving 1.411764706 + x = 1.678275602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.411764706' to each side of the equation. 1.411764706 + -1.411764706 + x = 1.678275602 + -1.411764706 Combine like terms: 1.411764706 + -1.411764706 = 0.000000000 0.000000000 + x = 1.678275602 + -1.411764706 x = 1.678275602 + -1.411764706 Combine like terms: 1.678275602 + -1.411764706 = 0.266510896 x = 0.266510896 Simplifying x = 0.266510896Subproblem 2
x + 1.411764706 = -1.678275602 Simplifying x + 1.411764706 = -1.678275602 Reorder the terms: 1.411764706 + x = -1.678275602 Solving 1.411764706 + x = -1.678275602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.411764706' to each side of the equation. 1.411764706 + -1.411764706 + x = -1.678275602 + -1.411764706 Combine like terms: 1.411764706 + -1.411764706 = 0.000000000 0.000000000 + x = -1.678275602 + -1.411764706 x = -1.678275602 + -1.411764706 Combine like terms: -1.678275602 + -1.411764706 = -3.090040308 x = -3.090040308 Simplifying x = -3.090040308Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.266510896, -3.090040308}
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