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Simplifying -0.7x2 + 11x + 3 = 0 Reorder the terms: 3 + 11x + -0.7x2 = 0 Solving 3 + 11x + -0.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -4.285714286 + -15.71428571x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -15.71428571x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -15.71428571x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -15.71428571x + x2 = 0 + 4.285714286 -15.71428571x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -15.71428571x + x2 = 4.285714286 The x term is -15.71428571x. Take half its coefficient (-7.857142855). Square it (61.73469384) and add it to both sides. Add '61.73469384' to each side of the equation. -15.71428571x + 61.73469384 + x2 = 4.285714286 + 61.73469384 Reorder the terms: 61.73469384 + -15.71428571x + x2 = 4.285714286 + 61.73469384 Combine like terms: 4.285714286 + 61.73469384 = 66.020408126 61.73469384 + -15.71428571x + x2 = 66.020408126 Factor a perfect square on the left side: (x + -7.857142855)(x + -7.857142855) = 66.020408126 Calculate the square root of the right side: 8.125294341 Break this problem into two subproblems by setting (x + -7.857142855) equal to 8.125294341 and -8.125294341.Subproblem 1
x + -7.857142855 = 8.125294341 Simplifying x + -7.857142855 = 8.125294341 Reorder the terms: -7.857142855 + x = 8.125294341 Solving -7.857142855 + x = 8.125294341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.857142855' to each side of the equation. -7.857142855 + 7.857142855 + x = 8.125294341 + 7.857142855 Combine like terms: -7.857142855 + 7.857142855 = 0.000000000 0.000000000 + x = 8.125294341 + 7.857142855 x = 8.125294341 + 7.857142855 Combine like terms: 8.125294341 + 7.857142855 = 15.982437196 x = 15.982437196 Simplifying x = 15.982437196Subproblem 2
x + -7.857142855 = -8.125294341 Simplifying x + -7.857142855 = -8.125294341 Reorder the terms: -7.857142855 + x = -8.125294341 Solving -7.857142855 + x = -8.125294341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.857142855' to each side of the equation. -7.857142855 + 7.857142855 + x = -8.125294341 + 7.857142855 Combine like terms: -7.857142855 + 7.857142855 = 0.000000000 0.000000000 + x = -8.125294341 + 7.857142855 x = -8.125294341 + 7.857142855 Combine like terms: -8.125294341 + 7.857142855 = -0.268151486 x = -0.268151486 Simplifying x = -0.268151486Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.982437196, -0.268151486}
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