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Simplifying 1x2 + -19x = -47 Reorder the terms: -19x + 1x2 = -47 Solving -19x + 1x2 = -47 Solving for variable 'x'. Reorder the terms: 47 + -19x + 1x2 = -47 + 47 Combine like terms: -47 + 47 = 0 47 + -19x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -19x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + -19x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -19x + x2 = 0 + -47 -19x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 -19x + x2 = -47 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 = -47 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -47 + 90.25 Combine like terms: -47 + 90.25 = 43.25 90.25 + -19x + x2 = 43.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + -9.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + -9.5 = 6.576473219 Simplifying x + -9.5 = 6.576473219 Reorder the terms: -9.5 + x = 6.576473219 Solving -9.5 + x = 6.576473219 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 = 6.576473219 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 6.576473219 + 9.5 x = 6.576473219 + 9.5 Combine like terms: 6.576473219 + 9.5 = 16.076473219 x = 16.076473219 Simplifying x = 16.076473219Subproblem 2
x + -9.5 = -6.576473219 Simplifying x + -9.5 = -6.576473219 Reorder the terms: -9.5 + x = -6.576473219 Solving -9.5 + x = -6.576473219 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 = -6.576473219 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -6.576473219 + 9.5 x = -6.576473219 + 9.5 Combine like terms: -6.576473219 + 9.5 = 2.923526781 x = 2.923526781 Simplifying x = 2.923526781Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.076473219, 2.923526781}
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