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Simplifying 10x2 + 19x + 3 = 0 Reorder the terms: 3 + 19x + 10x2 = 0 Solving 3 + 19x + 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'. 0.3 + 1.9x + x2 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + 1.9x + -0.3 + x2 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + 1.9x + x2 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + 1.9x + x2 = 0 + -0.3 1.9x + x2 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 1.9x + x2 = -0.3 The x term is 1.9x. Take half its coefficient (0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. 1.9x + 0.9025 + x2 = -0.3 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = -0.3 + 0.9025 Combine like terms: -0.3 + 0.9025 = 0.6025 0.9025 + 1.9x + x2 = 0.6025 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (x + 0.95) equal to 0.776208735 and -0.776208735.Subproblem 1
x + 0.95 = 0.776208735 Simplifying x + 0.95 = 0.776208735 Reorder the terms: 0.95 + x = 0.776208735 Solving 0.95 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = 0.776208735 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 0.776208735 + -0.95 x = 0.776208735 + -0.95 Combine like terms: 0.776208735 + -0.95 = -0.173791265 x = -0.173791265 Simplifying x = -0.173791265Subproblem 2
x + 0.95 = -0.776208735 Simplifying x + 0.95 = -0.776208735 Reorder the terms: 0.95 + x = -0.776208735 Solving 0.95 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = -0.776208735 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -0.776208735 + -0.95 x = -0.776208735 + -0.95 Combine like terms: -0.776208735 + -0.95 = -1.726208735 x = -1.726208735 Simplifying x = -1.726208735Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.173791265, -1.726208735}
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