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Simplifying (6x(3)) + -1(6x(8x)) = -11 Reorder the terms for easier multiplication: (6 * 3x) + -1(6x(8x)) = -11 Multiply 6 * 3 (18x) + -1(6x(8x)) = -11 Remove parenthesis around (8x) (18x) + -1(6x * 8x) = -11 Reorder the terms for easier multiplication: (18x) + -1(6 * 8x * x) = -11 Multiply 6 * 8 (18x) + -1(48x * x) = -11 Multiply x * x (18x) + -1(48x2) = -11 Remove parenthesis around (48x2) (18x) + -1 * 48x2 = -11 Multiply -1 * 48 (18x) + -48x2 = -11 Solving (18x) + -48x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + (18x) + -48x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + (18x) + -48x2 = 0 Begin completing the square. Divide all terms by -48 the coefficient of the squared term: Divide each side by '-48'. -0.2291666667 + (-0.375x) + x2 = 0 Move the constant term to the right: Add '0.2291666667' to each side of the equation. -0.2291666667 + (-0.375x) + 0.2291666667 + x2 = 0 + 0.2291666667 Reorder the terms: -0.2291666667 + 0.2291666667 + (-0.375x) + x2 = 0 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + (-0.375x) + x2 = 0 + 0.2291666667 (-0.375x) + x2 = 0 + 0.2291666667 Combine like terms: 0 + 0.2291666667 = 0.2291666667 (-0.375x) + x2 = 0.2291666667 The x term is (-0.375x). Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. (-0.375x) + 0.03515625 + x2 = 0.2291666667 + 0.03515625 Reorder the terms: 0.03515625 + (-0.375x) + x2 = 0.2291666667 + 0.03515625 Combine like terms: 0.2291666667 + 0.03515625 = 0.2643229167 0.03515625 + (-0.375x) + x2 = 0.2643229167 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.2643229167 Calculate the square root of the right side: 0.514123445 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.514123445 and -0.514123445.Subproblem 1
x + -0.1875 = 0.514123445 Simplifying x + -0.1875 = 0.514123445 Reorder the terms: -0.1875 + x = 0.514123445 Solving -0.1875 + x = 0.514123445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.514123445 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.514123445 + 0.1875 x = 0.514123445 + 0.1875 Combine like terms: 0.514123445 + 0.1875 = 0.701623445 x = 0.701623445 Simplifying x = 0.701623445Subproblem 2
x + -0.1875 = -0.514123445 Simplifying x + -0.1875 = -0.514123445 Reorder the terms: -0.1875 + x = -0.514123445 Solving -0.1875 + x = -0.514123445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.514123445 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.514123445 + 0.1875 x = -0.514123445 + 0.1875 Combine like terms: -0.514123445 + 0.1875 = -0.326623445 x = -0.326623445 Simplifying x = -0.326623445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.701623445, -0.326623445}
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