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Simplifying -16x2 + 22x = -50 Reorder the terms: 22x + -16x2 = -50 Solving 22x + -16x2 = -50 Solving for variable 'x'. Reorder the terms: 50 + 22x + -16x2 = -50 + 50 Combine like terms: -50 + 50 = 0 50 + 22x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 11x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 11x + -8x2)' equal to zero and attempt to solve: Simplifying 25 + 11x + -8x2 = 0 Solving 25 + 11x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -1.375x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -1.375x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -1.375x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -1.375x + x2 = 0 + 3.125 -1.375x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -1.375x + x2 = 3.125 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = 3.125 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = 3.125 + 0.47265625 Combine like terms: 3.125 + 0.47265625 = 3.59765625 0.47265625 + -1.375x + x2 = 3.59765625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 3.59765625 Calculate the square root of the right side: 1.896748863 Break this problem into two subproblems by setting (x + -0.6875) equal to 1.896748863 and -1.896748863.Subproblem 1
x + -0.6875 = 1.896748863 Simplifying x + -0.6875 = 1.896748863 Reorder the terms: -0.6875 + x = 1.896748863 Solving -0.6875 + x = 1.896748863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 1.896748863 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 1.896748863 + 0.6875 x = 1.896748863 + 0.6875 Combine like terms: 1.896748863 + 0.6875 = 2.584248863 x = 2.584248863 Simplifying x = 2.584248863Subproblem 2
x + -0.6875 = -1.896748863 Simplifying x + -0.6875 = -1.896748863 Reorder the terms: -0.6875 + x = -1.896748863 Solving -0.6875 + x = -1.896748863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -1.896748863 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -1.896748863 + 0.6875 x = -1.896748863 + 0.6875 Combine like terms: -1.896748863 + 0.6875 = -1.209248863 x = -1.209248863 Simplifying x = -1.209248863Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.584248863, -1.209248863}Solution
x = {2.584248863, -1.209248863}
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