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Simplifying -72y2 + 15y + 130 = 0 Reorder the terms: 130 + 15y + -72y2 = 0 Solving 130 + 15y + -72y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -72 the coefficient of the squared term: Divide each side by '-72'. -1.805555556 + -0.2083333333y + y2 = 0 Move the constant term to the right: Add '1.805555556' to each side of the equation. -1.805555556 + -0.2083333333y + 1.805555556 + y2 = 0 + 1.805555556 Reorder the terms: -1.805555556 + 1.805555556 + -0.2083333333y + y2 = 0 + 1.805555556 Combine like terms: -1.805555556 + 1.805555556 = 0.000000000 0.000000000 + -0.2083333333y + y2 = 0 + 1.805555556 -0.2083333333y + y2 = 0 + 1.805555556 Combine like terms: 0 + 1.805555556 = 1.805555556 -0.2083333333y + y2 = 1.805555556 The y term is -0.2083333333y. Take half its coefficient (-0.1041666667). Square it (0.01085069445) and add it to both sides. Add '0.01085069445' to each side of the equation. -0.2083333333y + 0.01085069445 + y2 = 1.805555556 + 0.01085069445 Reorder the terms: 0.01085069445 + -0.2083333333y + y2 = 1.805555556 + 0.01085069445 Combine like terms: 1.805555556 + 0.01085069445 = 1.81640625045 0.01085069445 + -0.2083333333y + y2 = 1.81640625045 Factor a perfect square on the left side: (y + -0.1041666667)(y + -0.1041666667) = 1.81640625045 Calculate the square root of the right side: 1.347741166 Break this problem into two subproblems by setting (y + -0.1041666667) equal to 1.347741166 and -1.347741166.Subproblem 1
y + -0.1041666667 = 1.347741166 Simplifying y + -0.1041666667 = 1.347741166 Reorder the terms: -0.1041666667 + y = 1.347741166 Solving -0.1041666667 + y = 1.347741166 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1041666667' to each side of the equation. -0.1041666667 + 0.1041666667 + y = 1.347741166 + 0.1041666667 Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000 0.0000000000 + y = 1.347741166 + 0.1041666667 y = 1.347741166 + 0.1041666667 Combine like terms: 1.347741166 + 0.1041666667 = 1.4519078327 y = 1.4519078327 Simplifying y = 1.4519078327Subproblem 2
y + -0.1041666667 = -1.347741166 Simplifying y + -0.1041666667 = -1.347741166 Reorder the terms: -0.1041666667 + y = -1.347741166 Solving -0.1041666667 + y = -1.347741166 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1041666667' to each side of the equation. -0.1041666667 + 0.1041666667 + y = -1.347741166 + 0.1041666667 Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000 0.0000000000 + y = -1.347741166 + 0.1041666667 y = -1.347741166 + 0.1041666667 Combine like terms: -1.347741166 + 0.1041666667 = -1.2435744993 y = -1.2435744993 Simplifying y = -1.2435744993Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.4519078327, -1.2435744993}
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