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Simplifying 19x = x2 + 12 Reorder the terms: 19x = 12 + x2 Solving 19x = 12 + x2 Solving for variable 'x'. Reorder the terms: -12 + 19x + -1x2 = 12 + x2 + -12 + -1x2 Reorder the terms: -12 + 19x + -1x2 = 12 + -12 + x2 + -1x2 Combine like terms: 12 + -12 = 0 -12 + 19x + -1x2 = 0 + x2 + -1x2 -12 + 19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + 19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -19x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -19x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -19x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -19x + x2 = 0 + -12 -19x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -19x + x2 = -12 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -12 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -12 + 90.25 Combine like terms: -12 + 90.25 = 78.25 90.25 + -19x + x2 = 78.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + -9.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + -9.5 = 8.845903006 Simplifying x + -9.5 = 8.845903006 Reorder the terms: -9.5 + x = 8.845903006 Solving -9.5 + x = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 8.845903006 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.845903006 + 9.5 x = 8.845903006 + 9.5 Combine like terms: 8.845903006 + 9.5 = 18.345903006 x = 18.345903006 Simplifying x = 18.345903006Subproblem 2
x + -9.5 = -8.845903006 Simplifying x + -9.5 = -8.845903006 Reorder the terms: -9.5 + x = -8.845903006 Solving -9.5 + x = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -8.845903006 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.845903006 + 9.5 x = -8.845903006 + 9.5 Combine like terms: -8.845903006 + 9.5 = 0.654096994 x = 0.654096994 Simplifying x = 0.654096994Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.345903006, 0.654096994}
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