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Simplifying 15x2 + 25x = 19 Reorder the terms: 25x + 15x2 = 19 Solving 25x + 15x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 25x + 15x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 25x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.266666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '1.266666667' to each side of the equation. -1.266666667 + 1.666666667x + 1.266666667 + x2 = 0 + 1.266666667 Reorder the terms: -1.266666667 + 1.266666667 + 1.666666667x + x2 = 0 + 1.266666667 Combine like terms: -1.266666667 + 1.266666667 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 1.266666667 1.666666667x + x2 = 0 + 1.266666667 Combine like terms: 0 + 1.266666667 = 1.266666667 1.666666667x + x2 = 1.266666667 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 1.266666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 1.266666667 + 0.6944444447 Combine like terms: 1.266666667 + 0.6944444447 = 1.9611111117 0.6944444447 + 1.666666667x + x2 = 1.9611111117 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.9611111117 Calculate the square root of the right side: 1.400396769 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.400396769 and -1.400396769.Subproblem 1
x + 0.8333333335 = 1.400396769 Simplifying x + 0.8333333335 = 1.400396769 Reorder the terms: 0.8333333335 + x = 1.400396769 Solving 0.8333333335 + x = 1.400396769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.400396769 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.400396769 + -0.8333333335 x = 1.400396769 + -0.8333333335 Combine like terms: 1.400396769 + -0.8333333335 = 0.5670634355 x = 0.5670634355 Simplifying x = 0.5670634355Subproblem 2
x + 0.8333333335 = -1.400396769 Simplifying x + 0.8333333335 = -1.400396769 Reorder the terms: 0.8333333335 + x = -1.400396769 Solving 0.8333333335 + x = -1.400396769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.400396769 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.400396769 + -0.8333333335 x = -1.400396769 + -0.8333333335 Combine like terms: -1.400396769 + -0.8333333335 = -2.2337301025 x = -2.2337301025 Simplifying x = -2.2337301025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5670634355, -2.2337301025}
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