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Simplifying 10x2 + 3x + -10 = 0 Reorder the terms: -10 + 3x + 10x2 = 0 Solving -10 + 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'. -1 + 0.3x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.3x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.3x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.3x + x2 = 0 + 1 0.3x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.3x + x2 = 1 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 = 1 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 1 + 0.0225 Combine like terms: 1 + 0.0225 = 1.0225 0.0225 + 0.3x + x2 = 1.0225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 1.0225 Calculate the square root of the right side: 1.011187421 Break this problem into two subproblems by setting (x + 0.15) equal to 1.011187421 and -1.011187421.Subproblem 1
x + 0.15 = 1.011187421 Simplifying x + 0.15 = 1.011187421 Reorder the terms: 0.15 + x = 1.011187421 Solving 0.15 + x = 1.011187421 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 = 1.011187421 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 1.011187421 + -0.15 x = 1.011187421 + -0.15 Combine like terms: 1.011187421 + -0.15 = 0.861187421 x = 0.861187421 Simplifying x = 0.861187421Subproblem 2
x + 0.15 = -1.011187421 Simplifying x + 0.15 = -1.011187421 Reorder the terms: 0.15 + x = -1.011187421 Solving 0.15 + x = -1.011187421 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 = -1.011187421 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -1.011187421 + -0.15 x = -1.011187421 + -0.15 Combine like terms: -1.011187421 + -0.15 = -1.161187421 x = -1.161187421 Simplifying x = -1.161187421Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.861187421, -1.161187421}
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