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Simplifying 10x2 + 9x + -4 = 0 Reorder the terms: -4 + 9x + 10x2 = 0 Solving -4 + 9x + 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'. -0.4 + 0.9x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.9x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.9x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.9x + x2 = 0 + 0.4 0.9x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.9x + x2 = 0.4 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 = 0.4 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 0.4 + 0.2025 Combine like terms: 0.4 + 0.2025 = 0.6025 0.2025 + 0.9x + x2 = 0.6025 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (x + 0.45) equal to 0.776208735 and -0.776208735.Subproblem 1
x + 0.45 = 0.776208735 Simplifying x + 0.45 = 0.776208735 Reorder the terms: 0.45 + x = 0.776208735 Solving 0.45 + x = 0.776208735 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 = 0.776208735 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 0.776208735 + -0.45 x = 0.776208735 + -0.45 Combine like terms: 0.776208735 + -0.45 = 0.326208735 x = 0.326208735 Simplifying x = 0.326208735Subproblem 2
x + 0.45 = -0.776208735 Simplifying x + 0.45 = -0.776208735 Reorder the terms: 0.45 + x = -0.776208735 Solving 0.45 + x = -0.776208735 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 = -0.776208735 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -0.776208735 + -0.45 x = -0.776208735 + -0.45 Combine like terms: -0.776208735 + -0.45 = -1.226208735 x = -1.226208735 Simplifying x = -1.226208735Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.326208735, -1.226208735}
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