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Simplifying 10X2 + 18X + -9 = 0 Reorder the terms: -9 + 18X + 10X2 = 0 Solving -9 + 18X + 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 + 1.8X + X2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 1.8X + 0.9 + X2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 1.8X + X2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 1.8X + X2 = 0 + 0.9 1.8X + X2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 1.8X + X2 = 0.9 The X term is 1.8X. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8X + 0.81 + X2 = 0.9 + 0.81 Reorder the terms: 0.81 + 1.8X + X2 = 0.9 + 0.81 Combine like terms: 0.9 + 0.81 = 1.71 0.81 + 1.8X + X2 = 1.71 Factor a perfect square on the left side: (X + 0.9)(X + 0.9) = 1.71 Calculate the square root of the right side: 1.307669683 Break this problem into two subproblems by setting (X + 0.9) equal to 1.307669683 and -1.307669683.Subproblem 1
X + 0.9 = 1.307669683 Simplifying X + 0.9 = 1.307669683 Reorder the terms: 0.9 + X = 1.307669683 Solving 0.9 + X = 1.307669683 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + X = 1.307669683 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + X = 1.307669683 + -0.9 X = 1.307669683 + -0.9 Combine like terms: 1.307669683 + -0.9 = 0.407669683 X = 0.407669683 Simplifying X = 0.407669683Subproblem 2
X + 0.9 = -1.307669683 Simplifying X + 0.9 = -1.307669683 Reorder the terms: 0.9 + X = -1.307669683 Solving 0.9 + X = -1.307669683 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + X = -1.307669683 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + X = -1.307669683 + -0.9 X = -1.307669683 + -0.9 Combine like terms: -1.307669683 + -0.9 = -2.207669683 X = -2.207669683 Simplifying X = -2.207669683Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.407669683, -2.207669683}
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