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Simplifying 10y2 + -30y + 13 = 0 Reorder the terms: 13 + -30y + 10y2 = 0 Solving 13 + -30y + 10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.3 + -3y + y2 = 0 Move the constant term to the right: Add '-1.3' to each side of the equation. 1.3 + -3y + -1.3 + y2 = 0 + -1.3 Reorder the terms: 1.3 + -1.3 + -3y + y2 = 0 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + -3y + y2 = 0 + -1.3 -3y + y2 = 0 + -1.3 Combine like terms: 0 + -1.3 = -1.3 -3y + y2 = -1.3 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = -1.3 + 2.25 Reorder the terms: 2.25 + -3y + y2 = -1.3 + 2.25 Combine like terms: -1.3 + 2.25 = 0.95 2.25 + -3y + y2 = 0.95 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 0.95 Calculate the square root of the right side: 0.974679434 Break this problem into two subproblems by setting (y + -1.5) equal to 0.974679434 and -0.974679434.Subproblem 1
y + -1.5 = 0.974679434 Simplifying y + -1.5 = 0.974679434 Reorder the terms: -1.5 + y = 0.974679434 Solving -1.5 + y = 0.974679434 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 0.974679434 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 0.974679434 + 1.5 y = 0.974679434 + 1.5 Combine like terms: 0.974679434 + 1.5 = 2.474679434 y = 2.474679434 Simplifying y = 2.474679434Subproblem 2
y + -1.5 = -0.974679434 Simplifying y + -1.5 = -0.974679434 Reorder the terms: -1.5 + y = -0.974679434 Solving -1.5 + y = -0.974679434 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -0.974679434 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -0.974679434 + 1.5 y = -0.974679434 + 1.5 Combine like terms: -0.974679434 + 1.5 = 0.525320566 y = 0.525320566 Simplifying y = 0.525320566Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.474679434, 0.525320566}
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