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Simplifying 10x2 + 3x + -225 = 0 Reorder the terms: -225 + 3x + 10x2 = 0 Solving -225 + 3x + 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'. -22.5 + 0.3x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 0.3x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 0.3x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 0.3x + x2 = 0 + 22.5 0.3x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 0.3x + x2 = 22.5 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 22.5 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 22.5 + 0.0225 Combine like terms: 22.5 + 0.0225 = 22.5225 0.0225 + 0.3x + x2 = 22.5225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 22.5225 Calculate the square root of the right side: 4.745787606 Break this problem into two subproblems by setting (x + 0.15) equal to 4.745787606 and -4.745787606.Subproblem 1
x + 0.15 = 4.745787606 Simplifying x + 0.15 = 4.745787606 Reorder the terms: 0.15 + x = 4.745787606 Solving 0.15 + x = 4.745787606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 4.745787606 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 4.745787606 + -0.15 x = 4.745787606 + -0.15 Combine like terms: 4.745787606 + -0.15 = 4.595787606 x = 4.595787606 Simplifying x = 4.595787606Subproblem 2
x + 0.15 = -4.745787606 Simplifying x + 0.15 = -4.745787606 Reorder the terms: 0.15 + x = -4.745787606 Solving 0.15 + x = -4.745787606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -4.745787606 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -4.745787606 + -0.15 x = -4.745787606 + -0.15 Combine like terms: -4.745787606 + -0.15 = -4.895787606 x = -4.895787606 Simplifying x = -4.895787606Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.595787606, -4.895787606}
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