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Simplifying -16x2 + 4.51x + 32.81 = 0 Reorder the terms: 32.81 + 4.51x + -16x2 = 0 Solving 32.81 + 4.51x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.050625 + -0.281875x + x2 = 0 Move the constant term to the right: Add '2.050625' to each side of the equation. -2.050625 + -0.281875x + 2.050625 + x2 = 0 + 2.050625 Reorder the terms: -2.050625 + 2.050625 + -0.281875x + x2 = 0 + 2.050625 Combine like terms: -2.050625 + 2.050625 = 0.000000 0.000000 + -0.281875x + x2 = 0 + 2.050625 -0.281875x + x2 = 0 + 2.050625 Combine like terms: 0 + 2.050625 = 2.050625 -0.281875x + x2 = 2.050625 The x term is -0.281875x. Take half its coefficient (-0.1409375). Square it (0.01986337891) and add it to both sides. Add '0.01986337891' to each side of the equation. -0.281875x + 0.01986337891 + x2 = 2.050625 + 0.01986337891 Reorder the terms: 0.01986337891 + -0.281875x + x2 = 2.050625 + 0.01986337891 Combine like terms: 2.050625 + 0.01986337891 = 2.07048837891 0.01986337891 + -0.281875x + x2 = 2.07048837891 Factor a perfect square on the left side: (x + -0.1409375)(x + -0.1409375) = 2.07048837891 Calculate the square root of the right side: 1.43891917 Break this problem into two subproblems by setting (x + -0.1409375) equal to 1.43891917 and -1.43891917.Subproblem 1
x + -0.1409375 = 1.43891917 Simplifying x + -0.1409375 = 1.43891917 Reorder the terms: -0.1409375 + x = 1.43891917 Solving -0.1409375 + x = 1.43891917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1409375' to each side of the equation. -0.1409375 + 0.1409375 + x = 1.43891917 + 0.1409375 Combine like terms: -0.1409375 + 0.1409375 = 0.0000000 0.0000000 + x = 1.43891917 + 0.1409375 x = 1.43891917 + 0.1409375 Combine like terms: 1.43891917 + 0.1409375 = 1.57985667 x = 1.57985667 Simplifying x = 1.57985667Subproblem 2
x + -0.1409375 = -1.43891917 Simplifying x + -0.1409375 = -1.43891917 Reorder the terms: -0.1409375 + x = -1.43891917 Solving -0.1409375 + x = -1.43891917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1409375' to each side of the equation. -0.1409375 + 0.1409375 + x = -1.43891917 + 0.1409375 Combine like terms: -0.1409375 + 0.1409375 = 0.0000000 0.0000000 + x = -1.43891917 + 0.1409375 x = -1.43891917 + 0.1409375 Combine like terms: -1.43891917 + 0.1409375 = -1.29798167 x = -1.29798167 Simplifying x = -1.29798167Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.57985667, -1.29798167}
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