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Simplifying 38318 + -196y2 = 782y Solving 38318 + -196y2 = 782y Solving for variable 'y'. Reorder the terms: 38318 + -782y + -196y2 = 782y + -782y Combine like terms: 782y + -782y = 0 38318 + -782y + -196y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(19159 + -391y + -98y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19159 + -391y + -98y2)' equal to zero and attempt to solve: Simplifying 19159 + -391y + -98y2 = 0 Solving 19159 + -391y + -98y2 = 0 Begin completing the square. Divide all terms by -98 the coefficient of the squared term: Divide each side by '-98'. -195.5 + 3.989795918y + y2 = 0 Move the constant term to the right: Add '195.5' to each side of the equation. -195.5 + 3.989795918y + 195.5 + y2 = 0 + 195.5 Reorder the terms: -195.5 + 195.5 + 3.989795918y + y2 = 0 + 195.5 Combine like terms: -195.5 + 195.5 = 0.0 0.0 + 3.989795918y + y2 = 0 + 195.5 3.989795918y + y2 = 0 + 195.5 Combine like terms: 0 + 195.5 = 195.5 3.989795918y + y2 = 195.5 The y term is 3.989795918y. Take half its coefficient (1.994897959). Square it (3.979617867) and add it to both sides. Add '3.979617867' to each side of the equation. 3.989795918y + 3.979617867 + y2 = 195.5 + 3.979617867 Reorder the terms: 3.979617867 + 3.989795918y + y2 = 195.5 + 3.979617867 Combine like terms: 195.5 + 3.979617867 = 199.479617867 3.979617867 + 3.989795918y + y2 = 199.479617867 Factor a perfect square on the left side: (y + 1.994897959)(y + 1.994897959) = 199.479617867 Calculate the square root of the right side: 14.123725354 Break this problem into two subproblems by setting (y + 1.994897959) equal to 14.123725354 and -14.123725354.Subproblem 1
y + 1.994897959 = 14.123725354 Simplifying y + 1.994897959 = 14.123725354 Reorder the terms: 1.994897959 + y = 14.123725354 Solving 1.994897959 + y = 14.123725354 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.994897959' to each side of the equation. 1.994897959 + -1.994897959 + y = 14.123725354 + -1.994897959 Combine like terms: 1.994897959 + -1.994897959 = 0.000000000 0.000000000 + y = 14.123725354 + -1.994897959 y = 14.123725354 + -1.994897959 Combine like terms: 14.123725354 + -1.994897959 = 12.128827395 y = 12.128827395 Simplifying y = 12.128827395Subproblem 2
y + 1.994897959 = -14.123725354 Simplifying y + 1.994897959 = -14.123725354 Reorder the terms: 1.994897959 + y = -14.123725354 Solving 1.994897959 + y = -14.123725354 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.994897959' to each side of the equation. 1.994897959 + -1.994897959 + y = -14.123725354 + -1.994897959 Combine like terms: 1.994897959 + -1.994897959 = 0.000000000 0.000000000 + y = -14.123725354 + -1.994897959 y = -14.123725354 + -1.994897959 Combine like terms: -14.123725354 + -1.994897959 = -16.118623313 y = -16.118623313 Simplifying y = -16.118623313Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.128827395, -16.118623313}Solution
y = {12.128827395, -16.118623313}
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