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Simplifying 0.1265x2 + -2x + -1 = 0 Reorder the terms: -1 + -2x + 0.1265x2 = 0 Solving -1 + -2x + 0.1265x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1265 the coefficient of the squared term: Divide each side by '0.1265'. -7.90513834 + -15.81027668x + x2 = 0 Move the constant term to the right: Add '7.90513834' to each side of the equation. -7.90513834 + -15.81027668x + 7.90513834 + x2 = 0 + 7.90513834 Reorder the terms: -7.90513834 + 7.90513834 + -15.81027668x + x2 = 0 + 7.90513834 Combine like terms: -7.90513834 + 7.90513834 = 0.00000000 0.00000000 + -15.81027668x + x2 = 0 + 7.90513834 -15.81027668x + x2 = 0 + 7.90513834 Combine like terms: 0 + 7.90513834 = 7.90513834 -15.81027668x + x2 = 7.90513834 The x term is -15.81027668x. Take half its coefficient (-7.90513834). Square it (62.49121217) and add it to both sides. Add '62.49121217' to each side of the equation. -15.81027668x + 62.49121217 + x2 = 7.90513834 + 62.49121217 Reorder the terms: 62.49121217 + -15.81027668x + x2 = 7.90513834 + 62.49121217 Combine like terms: 7.90513834 + 62.49121217 = 70.39635051 62.49121217 + -15.81027668x + x2 = 70.39635051 Factor a perfect square on the left side: (x + -7.90513834)(x + -7.90513834) = 70.39635051 Calculate the square root of the right side: 8.390253304 Break this problem into two subproblems by setting (x + -7.90513834) equal to 8.390253304 and -8.390253304.Subproblem 1
x + -7.90513834 = 8.390253304 Simplifying x + -7.90513834 = 8.390253304 Reorder the terms: -7.90513834 + x = 8.390253304 Solving -7.90513834 + x = 8.390253304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.90513834' to each side of the equation. -7.90513834 + 7.90513834 + x = 8.390253304 + 7.90513834 Combine like terms: -7.90513834 + 7.90513834 = 0.00000000 0.00000000 + x = 8.390253304 + 7.90513834 x = 8.390253304 + 7.90513834 Combine like terms: 8.390253304 + 7.90513834 = 16.295391644 x = 16.295391644 Simplifying x = 16.295391644Subproblem 2
x + -7.90513834 = -8.390253304 Simplifying x + -7.90513834 = -8.390253304 Reorder the terms: -7.90513834 + x = -8.390253304 Solving -7.90513834 + x = -8.390253304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.90513834' to each side of the equation. -7.90513834 + 7.90513834 + x = -8.390253304 + 7.90513834 Combine like terms: -7.90513834 + 7.90513834 = 0.00000000 0.00000000 + x = -8.390253304 + 7.90513834 x = -8.390253304 + 7.90513834 Combine like terms: -8.390253304 + 7.90513834 = -0.485114964 x = -0.485114964 Simplifying x = -0.485114964Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.295391644, -0.485114964}
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