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Simplifying 0 = -6x2 + 5x + 7 Reorder the terms: 0 = 7 + 5x + -6x2 Solving 0 = 7 + 5x + -6x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -5x + 6x2 = 7 + 5x + -6x2 + -7 + -5x + 6x2 Reorder the terms: -7 + -5x + 6x2 = 7 + -7 + 5x + -5x + -6x2 + 6x2 Combine like terms: 7 + -7 = 0 -7 + -5x + 6x2 = 0 + 5x + -5x + -6x2 + 6x2 -7 + -5x + 6x2 = 5x + -5x + -6x2 + 6x2 Combine like terms: 5x + -5x = 0 -7 + -5x + 6x2 = 0 + -6x2 + 6x2 -7 + -5x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -7 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -0.8333333333x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -0.8333333333x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -0.8333333333x + x2 = 0 + 1.166666667 -0.8333333333x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -0.8333333333x + x2 = 1.166666667 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 1.166666667 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 1.166666667 + 0.1736111111 Combine like terms: 1.166666667 + 0.1736111111 = 1.3402777781 0.1736111111 + -0.8333333333x + x2 = 1.3402777781 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 1.3402777781 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 1.157703666 and -1.157703666.Subproblem 1
x + -0.4166666667 = 1.157703666 Simplifying x + -0.4166666667 = 1.157703666 Reorder the terms: -0.4166666667 + x = 1.157703666 Solving -0.4166666667 + x = 1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 1.157703666 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 1.157703666 + 0.4166666667 x = 1.157703666 + 0.4166666667 Combine like terms: 1.157703666 + 0.4166666667 = 1.5743703327 x = 1.5743703327 Simplifying x = 1.5743703327Subproblem 2
x + -0.4166666667 = -1.157703666 Simplifying x + -0.4166666667 = -1.157703666 Reorder the terms: -0.4166666667 + x = -1.157703666 Solving -0.4166666667 + x = -1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -1.157703666 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -1.157703666 + 0.4166666667 x = -1.157703666 + 0.4166666667 Combine like terms: -1.157703666 + 0.4166666667 = -0.7410369993 x = -0.7410369993 Simplifying x = -0.7410369993Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5743703327, -0.7410369993}
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