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Simplifying -5x2 + 6x + 9 = 0 Reorder the terms: 9 + 6x + -5x2 = 0 Solving 9 + 6x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.8 + -1.2x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -1.2x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -1.2x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -1.2x + x2 = 0 + 1.8 -1.2x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -1.2x + x2 = 1.8 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 = 1.8 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 1.8 + 0.36 Combine like terms: 1.8 + 0.36 = 2.16 0.36 + -1.2x + x2 = 2.16 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (x + -0.6) equal to 1.469693846 and -1.469693846.Subproblem 1
x + -0.6 = 1.469693846 Simplifying x + -0.6 = 1.469693846 Reorder the terms: -0.6 + x = 1.469693846 Solving -0.6 + x = 1.469693846 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 = 1.469693846 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.469693846 + 0.6 x = 1.469693846 + 0.6 Combine like terms: 1.469693846 + 0.6 = 2.069693846 x = 2.069693846 Simplifying x = 2.069693846Subproblem 2
x + -0.6 = -1.469693846 Simplifying x + -0.6 = -1.469693846 Reorder the terms: -0.6 + x = -1.469693846 Solving -0.6 + x = -1.469693846 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 = -1.469693846 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.469693846 + 0.6 x = -1.469693846 + 0.6 Combine like terms: -1.469693846 + 0.6 = -0.869693846 x = -0.869693846 Simplifying x = -0.869693846Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.069693846, -0.869693846}
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