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Simplifying -10x2 + 9x + 1 = 1.8 Reorder the terms: 1 + 9x + -10x2 = 1.8 Solving 1 + 9x + -10x2 = 1.8 Solving for variable 'x'. Reorder the terms: 1 + -1.8 + 9x + -10x2 = 1.8 + -1.8 Combine like terms: 1 + -1.8 = -0.8 -0.8 + 9x + -10x2 = 1.8 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 -0.8 + 9x + -10x2 = 0.0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 0.08 + -0.9x + x2 = 0.0 Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + -0.9x + -0.08 + x2 = 0.0 + -0.08 Reorder the terms: 0.08 + -0.08 + -0.9x + x2 = 0.0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + -0.9x + x2 = 0.0 + -0.08 -0.9x + x2 = 0.0 + -0.08 Combine like terms: 0.0 + -0.08 = -0.08 -0.9x + x2 = -0.08 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = -0.08 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = -0.08 + 0.2025 Combine like terms: -0.08 + 0.2025 = 0.1225 0.2025 + -0.9x + x2 = 0.1225 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 0.1225 Calculate the square root of the right side: 0.35 Break this problem into two subproblems by setting (x + -0.45) equal to 0.35 and -0.35.Subproblem 1
x + -0.45 = 0.35 Simplifying x + -0.45 = 0.35 Reorder the terms: -0.45 + x = 0.35 Solving -0.45 + x = 0.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 0.35 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.35 + 0.45 x = 0.35 + 0.45 Combine like terms: 0.35 + 0.45 = 0.8 x = 0.8 Simplifying x = 0.8Subproblem 2
x + -0.45 = -0.35 Simplifying x + -0.45 = -0.35 Reorder the terms: -0.45 + x = -0.35 Solving -0.45 + x = -0.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -0.35 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.35 + 0.45 x = -0.35 + 0.45 Combine like terms: -0.35 + 0.45 = 0.1 x = 0.1 Simplifying x = 0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8, 0.1}
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