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Simplifying 6x2 = 7 + -5x Solving 6x2 = 7 + -5x Solving for variable 'x'. Reorder the terms: -7 + 5x + 6x2 = 7 + -5x + -7 + 5x Reorder the terms: -7 + 5x + 6x2 = 7 + -7 + -5x + 5x Combine like terms: 7 + -7 = 0 -7 + 5x + 6x2 = 0 + -5x + 5x -7 + 5x + 6x2 = -5x + 5x Combine like terms: -5x + 5x = 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 = 0.7410369993 x = 0.7410369993 Simplifying x = 0.7410369993Subproblem 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 = -1.5743703327 x = -1.5743703327 Simplifying x = -1.5743703327Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7410369993, -1.5743703327}
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