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Simplifying 10x2 + -6x + -9 = 0 Reorder the terms: -9 + -6x + 10x2 = 0 Solving -9 + -6x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + -0.6x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -0.6x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -0.6x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -0.6x + x2 = 0 + 0.9 -0.6x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -0.6x + x2 = 0.9 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.9 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.9 + 0.09 Combine like terms: 0.9 + 0.09 = 0.99 0.09 + -0.6x + x2 = 0.99 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.99 Calculate the square root of the right side: 0.994987437 Break this problem into two subproblems by setting (x + -0.3) equal to 0.994987437 and -0.994987437.Subproblem 1
x + -0.3 = 0.994987437 Simplifying x + -0.3 = 0.994987437 Reorder the terms: -0.3 + x = 0.994987437 Solving -0.3 + x = 0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.994987437 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.994987437 + 0.3 x = 0.994987437 + 0.3 Combine like terms: 0.994987437 + 0.3 = 1.294987437 x = 1.294987437 Simplifying x = 1.294987437Subproblem 2
x + -0.3 = -0.994987437 Simplifying x + -0.3 = -0.994987437 Reorder the terms: -0.3 + x = -0.994987437 Solving -0.3 + x = -0.994987437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.994987437 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.994987437 + 0.3 x = -0.994987437 + 0.3 Combine like terms: -0.994987437 + 0.3 = -0.694987437 x = -0.694987437 Simplifying x = -0.694987437Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.294987437, -0.694987437}
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