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Simplifying 10x2 + -12x + -9 = 0 Reorder the terms: -9 + -12x + 10x2 = 0 Solving -9 + -12x + 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 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -1.2x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -1.2x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -1.2x + x2 = 0 + 0.9 -1.2x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -1.2x + x2 = 0.9 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 = 0.9 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.9 + 0.36 Combine like terms: 0.9 + 0.36 = 1.26 0.36 + -1.2x + x2 = 1.26 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.26 Calculate the square root of the right side: 1.122497216 Break this problem into two subproblems by setting (x + -0.6) equal to 1.122497216 and -1.122497216.Subproblem 1
x + -0.6 = 1.122497216 Simplifying x + -0.6 = 1.122497216 Reorder the terms: -0.6 + x = 1.122497216 Solving -0.6 + x = 1.122497216 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 = 1.122497216 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.122497216 + 0.6 x = 1.122497216 + 0.6 Combine like terms: 1.122497216 + 0.6 = 1.722497216 x = 1.722497216 Simplifying x = 1.722497216Subproblem 2
x + -0.6 = -1.122497216 Simplifying x + -0.6 = -1.122497216 Reorder the terms: -0.6 + x = -1.122497216 Solving -0.6 + x = -1.122497216 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 = -1.122497216 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.122497216 + 0.6 x = -1.122497216 + 0.6 Combine like terms: -1.122497216 + 0.6 = -0.522497216 x = -0.522497216 Simplifying x = -0.522497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.722497216, -0.522497216}
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