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Simplifying x(6x + -7) = 130 Reorder the terms: x(-7 + 6x) = 130 (-7 * x + 6x * x) = 130 (-7x + 6x2) = 130 Solving -7x + 6x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + -7x + 6x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -21.66666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '21.66666667' to each side of the equation. -21.66666667 + -1.166666667x + 21.66666667 + x2 = 0 + 21.66666667 Reorder the terms: -21.66666667 + 21.66666667 + -1.166666667x + x2 = 0 + 21.66666667 Combine like terms: -21.66666667 + 21.66666667 = 0.00000000 0.00000000 + -1.166666667x + x2 = 0 + 21.66666667 -1.166666667x + x2 = 0 + 21.66666667 Combine like terms: 0 + 21.66666667 = 21.66666667 -1.166666667x + x2 = 21.66666667 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 21.66666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 21.66666667 + 0.3402777780 Combine like terms: 21.66666667 + 0.3402777780 = 22.006944448 0.3402777780 + -1.166666667x + x2 = 22.006944448 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 22.006944448 Calculate the square root of the right side: 4.691155982 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 4.691155982 and -4.691155982.Subproblem 1
x + -0.5833333335 = 4.691155982 Simplifying x + -0.5833333335 = 4.691155982 Reorder the terms: -0.5833333335 + x = 4.691155982 Solving -0.5833333335 + x = 4.691155982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 4.691155982 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 4.691155982 + 0.5833333335 x = 4.691155982 + 0.5833333335 Combine like terms: 4.691155982 + 0.5833333335 = 5.2744893155 x = 5.2744893155 Simplifying x = 5.2744893155Subproblem 2
x + -0.5833333335 = -4.691155982 Simplifying x + -0.5833333335 = -4.691155982 Reorder the terms: -0.5833333335 + x = -4.691155982 Solving -0.5833333335 + x = -4.691155982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -4.691155982 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -4.691155982 + 0.5833333335 x = -4.691155982 + 0.5833333335 Combine like terms: -4.691155982 + 0.5833333335 = -4.1078226485 x = -4.1078226485 Simplifying x = -4.1078226485Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.2744893155, -4.1078226485}
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