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Simplifying 5x2 + 19x + 15 = 0 Reorder the terms: 15 + 19x + 5x2 = 0 Solving 15 + 19x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + 3.8x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.8x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3.8x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.8x + x2 = 0 + -3 3.8x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.8x + x2 = -3 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = -3 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = -3 + 3.61 Combine like terms: -3 + 3.61 = 0.61 3.61 + 3.8x + x2 = 0.61 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 0.61 Calculate the square root of the right side: 0.781024968 Break this problem into two subproblems by setting (x + 1.9) equal to 0.781024968 and -0.781024968.Subproblem 1
x + 1.9 = 0.781024968 Simplifying x + 1.9 = 0.781024968 Reorder the terms: 1.9 + x = 0.781024968 Solving 1.9 + x = 0.781024968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 0.781024968 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 0.781024968 + -1.9 x = 0.781024968 + -1.9 Combine like terms: 0.781024968 + -1.9 = -1.118975032 x = -1.118975032 Simplifying x = -1.118975032Subproblem 2
x + 1.9 = -0.781024968 Simplifying x + 1.9 = -0.781024968 Reorder the terms: 1.9 + x = -0.781024968 Solving 1.9 + x = -0.781024968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -0.781024968 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -0.781024968 + -1.9 x = -0.781024968 + -1.9 Combine like terms: -0.781024968 + -1.9 = -2.681024968 x = -2.681024968 Simplifying x = -2.681024968Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.118975032, -2.681024968}
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