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Simplifying -5x2 + 7x + 6 = x Reorder the terms: 6 + 7x + -5x2 = x Solving 6 + 7x + -5x2 = x Solving for variable 'x'. Reorder the terms: 6 + 7x + -1x + -5x2 = x + -1x Combine like terms: 7x + -1x = 6x 6 + 6x + -5x2 = x + -1x Combine like terms: x + -1x = 0 6 + 6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + -1.2x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1.2x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1.2x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1.2x + x2 = 0 + 1.2 -1.2x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1.2x + x2 = 1.2 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 1.2 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 1.2 + 0.36 Combine like terms: 1.2 + 0.36 = 1.56 0.36 + -1.2x + x2 = 1.56 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (x + -0.6) equal to 1.2489996 and -1.2489996.Subproblem 1
x + -0.6 = 1.2489996 Simplifying x + -0.6 = 1.2489996 Reorder the terms: -0.6 + x = 1.2489996 Solving -0.6 + x = 1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.2489996 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.2489996 + 0.6 x = 1.2489996 + 0.6 Combine like terms: 1.2489996 + 0.6 = 1.8489996 x = 1.8489996 Simplifying x = 1.8489996Subproblem 2
x + -0.6 = -1.2489996 Simplifying x + -0.6 = -1.2489996 Reorder the terms: -0.6 + x = -1.2489996 Solving -0.6 + x = -1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.2489996 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.2489996 + 0.6 x = -1.2489996 + 0.6 Combine like terms: -1.2489996 + 0.6 = -0.6489996 x = -0.6489996 Simplifying x = -0.6489996Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8489996, -0.6489996}
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