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Simplifying -167x2 + x + 63 = 0 Reorder the terms: 63 + x + -167x2 = 0 Solving 63 + x + -167x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -167 the coefficient of the squared term: Divide each side by '-167'. -0.377245509 + -0.005988023952x + x2 = 0 Move the constant term to the right: Add '0.377245509' to each side of the equation. -0.377245509 + -0.005988023952x + 0.377245509 + x2 = 0 + 0.377245509 Reorder the terms: -0.377245509 + 0.377245509 + -0.005988023952x + x2 = 0 + 0.377245509 Combine like terms: -0.377245509 + 0.377245509 = 0.000000000 0.000000000 + -0.005988023952x + x2 = 0 + 0.377245509 -0.005988023952x + x2 = 0 + 0.377245509 Combine like terms: 0 + 0.377245509 = 0.377245509 -0.005988023952x + x2 = 0.377245509 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. -0.005988023952x + 0.25 + x2 = 0.377245509 + 0.25 Reorder the terms: 0.25 + -0.005988023952x + x2 = 0.377245509 + 0.25 Combine like terms: 0.377245509 + 0.25 = 0.627245509 0.25 + -0.005988023952x + x2 = 0.627245509 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.627245509 Calculate the square root of the right side: 0.791988326 Break this problem into two subproblems by setting (x + 0.5) equal to 0.791988326 and -0.791988326.Subproblem 1
x + 0.5 = 0.791988326 Simplifying x + 0.5 = 0.791988326 Reorder the terms: 0.5 + x = 0.791988326 Solving 0.5 + x = 0.791988326 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 = 0.791988326 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.791988326 + -0.5 x = 0.791988326 + -0.5 Combine like terms: 0.791988326 + -0.5 = 0.291988326 x = 0.291988326 Simplifying x = 0.291988326Subproblem 2
x + 0.5 = -0.791988326 Simplifying x + 0.5 = -0.791988326 Reorder the terms: 0.5 + x = -0.791988326 Solving 0.5 + x = -0.791988326 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 = -0.791988326 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.791988326 + -0.5 x = -0.791988326 + -0.5 Combine like terms: -0.791988326 + -0.5 = -1.291988326 x = -1.291988326 Simplifying x = -1.291988326Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.291988326, -1.291988326}
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