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Simplifying 70x2 + -105x + -16 = 0 Reorder the terms: -16 + -105x + 70x2 = 0 Solving -16 + -105x + 70x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. -0.2285714286 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.2285714286' to each side of the equation. -0.2285714286 + -1.5x + 0.2285714286 + x2 = 0 + 0.2285714286 Reorder the terms: -0.2285714286 + 0.2285714286 + -1.5x + x2 = 0 + 0.2285714286 Combine like terms: -0.2285714286 + 0.2285714286 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + 0.2285714286 -1.5x + x2 = 0 + 0.2285714286 Combine like terms: 0 + 0.2285714286 = 0.2285714286 -1.5x + x2 = 0.2285714286 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.2285714286 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.2285714286 + 0.5625 Combine like terms: 0.2285714286 + 0.5625 = 0.7910714286 0.5625 + -1.5x + x2 = 0.7910714286 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.7910714286 Calculate the square root of the right side: 0.889421963 Break this problem into two subproblems by setting (x + -0.75) equal to 0.889421963 and -0.889421963.Subproblem 1
x + -0.75 = 0.889421963 Simplifying x + -0.75 = 0.889421963 Reorder the terms: -0.75 + x = 0.889421963 Solving -0.75 + x = 0.889421963 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.889421963 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.889421963 + 0.75 x = 0.889421963 + 0.75 Combine like terms: 0.889421963 + 0.75 = 1.639421963 x = 1.639421963 Simplifying x = 1.639421963Subproblem 2
x + -0.75 = -0.889421963 Simplifying x + -0.75 = -0.889421963 Reorder the terms: -0.75 + x = -0.889421963 Solving -0.75 + x = -0.889421963 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.889421963 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.889421963 + 0.75 x = -0.889421963 + 0.75 Combine like terms: -0.889421963 + 0.75 = -0.139421963 x = -0.139421963 Simplifying x = -0.139421963Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.639421963, -0.139421963}
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