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Simplifying 1.025x2 + -4x + 20 = -2.125x2 + 6x + 40 Reorder the terms: 20 + -4x + 1.025x2 = -2.125x2 + 6x + 40 Reorder the terms: 20 + -4x + 1.025x2 = 40 + 6x + -2.125x2 Solving 20 + -4x + 1.025x2 = 40 + 6x + -2.125x2 Solving for variable 'x'. Reorder the terms: 20 + -40 + -4x + -6x + 1.025x2 + 2.125x2 = 40 + 6x + -2.125x2 + -40 + -6x + 2.125x2 Combine like terms: 20 + -40 = -20 -20 + -4x + -6x + 1.025x2 + 2.125x2 = 40 + 6x + -2.125x2 + -40 + -6x + 2.125x2 Combine like terms: -4x + -6x = -10x -20 + -10x + 1.025x2 + 2.125x2 = 40 + 6x + -2.125x2 + -40 + -6x + 2.125x2 Combine like terms: 1.025x2 + 2.125x2 = 3.15x2 -20 + -10x + 3.15x2 = 40 + 6x + -2.125x2 + -40 + -6x + 2.125x2 Reorder the terms: -20 + -10x + 3.15x2 = 40 + -40 + 6x + -6x + -2.125x2 + 2.125x2 Combine like terms: 40 + -40 = 0 -20 + -10x + 3.15x2 = 0 + 6x + -6x + -2.125x2 + 2.125x2 -20 + -10x + 3.15x2 = 6x + -6x + -2.125x2 + 2.125x2 Combine like terms: 6x + -6x = 0 -20 + -10x + 3.15x2 = 0 + -2.125x2 + 2.125x2 -20 + -10x + 3.15x2 = -2.125x2 + 2.125x2 Combine like terms: -2.125x2 + 2.125x2 = 0.000 -20 + -10x + 3.15x2 = 0.000 Begin completing the square. Divide all terms by 3.15 the coefficient of the squared term: Divide each side by '3.15'. -6.349206349 + -3.174603175x + x2 = 0.0 Move the constant term to the right: Add '6.349206349' to each side of the equation. -6.349206349 + -3.174603175x + 6.349206349 + x2 = 0.0 + 6.349206349 Reorder the terms: -6.349206349 + 6.349206349 + -3.174603175x + x2 = 0.0 + 6.349206349 Combine like terms: -6.349206349 + 6.349206349 = 0.000000000 0.000000000 + -3.174603175x + x2 = 0.0 + 6.349206349 -3.174603175x + x2 = 0.0 + 6.349206349 Combine like terms: 0.0 + 6.349206349 = 6.349206349 -3.174603175x + x2 = 6.349206349 The x term is -3.174603175x. Take half its coefficient (-1.587301588). Square it (2.519526331) and add it to both sides. Add '2.519526331' to each side of the equation. -3.174603175x + 2.519526331 + x2 = 6.349206349 + 2.519526331 Reorder the terms: 2.519526331 + -3.174603175x + x2 = 6.349206349 + 2.519526331 Combine like terms: 6.349206349 + 2.519526331 = 8.86873268 2.519526331 + -3.174603175x + x2 = 8.86873268 Factor a perfect square on the left side: (x + -1.587301588)(x + -1.587301588) = 8.86873268 Calculate the square root of the right side: 2.978041753 Break this problem into two subproblems by setting (x + -1.587301588) equal to 2.978041753 and -2.978041753.Subproblem 1
x + -1.587301588 = 2.978041753 Simplifying x + -1.587301588 = 2.978041753 Reorder the terms: -1.587301588 + x = 2.978041753 Solving -1.587301588 + x = 2.978041753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.587301588' to each side of the equation. -1.587301588 + 1.587301588 + x = 2.978041753 + 1.587301588 Combine like terms: -1.587301588 + 1.587301588 = 0.000000000 0.000000000 + x = 2.978041753 + 1.587301588 x = 2.978041753 + 1.587301588 Combine like terms: 2.978041753 + 1.587301588 = 4.565343341 x = 4.565343341 Simplifying x = 4.565343341Subproblem 2
x + -1.587301588 = -2.978041753 Simplifying x + -1.587301588 = -2.978041753 Reorder the terms: -1.587301588 + x = -2.978041753 Solving -1.587301588 + x = -2.978041753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.587301588' to each side of the equation. -1.587301588 + 1.587301588 + x = -2.978041753 + 1.587301588 Combine like terms: -1.587301588 + 1.587301588 = 0.000000000 0.000000000 + x = -2.978041753 + 1.587301588 x = -2.978041753 + 1.587301588 Combine like terms: -2.978041753 + 1.587301588 = -1.390740165 x = -1.390740165 Simplifying x = -1.390740165Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.565343341, -1.390740165}
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