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Simplifying 10x2 + 10x + -19 = 0 Reorder the terms: -19 + 10x + 10x2 = 0 Solving -19 + 10x + 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'. -1.9 + x + x2 = 0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + x + 1.9 + x2 = 0 + 1.9 Reorder the terms: -1.9 + 1.9 + x + x2 = 0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x + x2 = 0 + 1.9 x + x2 = 0 + 1.9 Combine like terms: 0 + 1.9 = 1.9 x + x2 = 1.9 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.9 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.9 + 0.25 Combine like terms: 1.9 + 0.25 = 2.15 1.25 + x2 = 2.15 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.15 Calculate the square root of the right side: 1.46628783 Break this problem into two subproblems by setting (x + 0.5) equal to 1.46628783 and -1.46628783.Subproblem 1
x + 0.5 = 1.46628783 Simplifying x + 0.5 = 1.46628783 Reorder the terms: 0.5 + x = 1.46628783 Solving 0.5 + x = 1.46628783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.46628783 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.46628783 + -0.5 x = 1.46628783 + -0.5 Combine like terms: 1.46628783 + -0.5 = 0.96628783 x = 0.96628783 Simplifying x = 0.96628783Subproblem 2
x + 0.5 = -1.46628783 Simplifying x + 0.5 = -1.46628783 Reorder the terms: 0.5 + x = -1.46628783 Solving 0.5 + x = -1.46628783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.46628783 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.46628783 + -0.5 x = -1.46628783 + -0.5 Combine like terms: -1.46628783 + -0.5 = -1.96628783 x = -1.96628783 Simplifying x = -1.96628783Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96628783, -1.96628783}
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