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Simplifying 6x2 = -10x + -1 Reorder the terms: 6x2 = -1 + -10x Solving 6x2 = -1 + -10x Solving for variable 'x'. Reorder the terms: 1 + 10x + 6x2 = -1 + -10x + 1 + 10x Reorder the terms: 1 + 10x + 6x2 = -1 + 1 + -10x + 10x Combine like terms: -1 + 1 = 0 1 + 10x + 6x2 = 0 + -10x + 10x 1 + 10x + 6x2 = -10x + 10x Combine like terms: -10x + 10x = 0 1 + 10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 1.666666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 1.666666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + -0.1666666667 1.666666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 1.666666667x + x2 = -0.1666666667 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = -0.1666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -0.1666666667 + 0.6944444447 Combine like terms: -0.1666666667 + 0.6944444447 = 0.527777778 0.6944444447 + 1.666666667x + x2 = 0.527777778 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 0.527777778 Calculate the square root of the right side: 0.726483157 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 0.726483157 and -0.726483157.Subproblem 1
x + 0.8333333335 = 0.726483157 Simplifying x + 0.8333333335 = 0.726483157 Reorder the terms: 0.8333333335 + x = 0.726483157 Solving 0.8333333335 + x = 0.726483157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 0.726483157 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 0.726483157 + -0.8333333335 x = 0.726483157 + -0.8333333335 Combine like terms: 0.726483157 + -0.8333333335 = -0.1068501765 x = -0.1068501765 Simplifying x = -0.1068501765Subproblem 2
x + 0.8333333335 = -0.726483157 Simplifying x + 0.8333333335 = -0.726483157 Reorder the terms: 0.8333333335 + x = -0.726483157 Solving 0.8333333335 + x = -0.726483157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -0.726483157 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -0.726483157 + -0.8333333335 x = -0.726483157 + -0.8333333335 Combine like terms: -0.726483157 + -0.8333333335 = -1.5598164905 x = -1.5598164905 Simplifying x = -1.5598164905Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1068501765, -1.5598164905}
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