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Simplifying 6x2 + -10x + -7 = 0 Reorder the terms: -7 + -10x + 6x2 = 0 Solving -7 + -10x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -1.666666667x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -1.666666667x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 1.166666667 -1.666666667x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -1.666666667x + x2 = 1.166666667 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 = 1.166666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 1.166666667 + 0.6944444447 Combine like terms: 1.166666667 + 0.6944444447 = 1.8611111117 0.6944444447 + -1.666666667x + x2 = 1.8611111117 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 1.8611111117 Calculate the square root of the right side: 1.364225462 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.364225462 and -1.364225462.Subproblem 1
x + -0.8333333335 = 1.364225462 Simplifying x + -0.8333333335 = 1.364225462 Reorder the terms: -0.8333333335 + x = 1.364225462 Solving -0.8333333335 + x = 1.364225462 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 = 1.364225462 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.364225462 + 0.8333333335 x = 1.364225462 + 0.8333333335 Combine like terms: 1.364225462 + 0.8333333335 = 2.1975587955 x = 2.1975587955 Simplifying x = 2.1975587955Subproblem 2
x + -0.8333333335 = -1.364225462 Simplifying x + -0.8333333335 = -1.364225462 Reorder the terms: -0.8333333335 + x = -1.364225462 Solving -0.8333333335 + x = -1.364225462 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 = -1.364225462 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.364225462 + 0.8333333335 x = -1.364225462 + 0.8333333335 Combine like terms: -1.364225462 + 0.8333333335 = -0.5308921285 x = -0.5308921285 Simplifying x = -0.5308921285Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1975587955, -0.5308921285}
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