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Simplifying 10z2 + -19z + -48 = 0 Reorder the terms: -48 + -19z + 10z2 = 0 Solving -48 + -19z + 10z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -4.8 + -1.9z + z2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -1.9z + 4.8 + z2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -1.9z + z2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -1.9z + z2 = 0 + 4.8 -1.9z + z2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -1.9z + z2 = 4.8 The z term is -1.9z. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9z + 0.9025 + z2 = 4.8 + 0.9025 Reorder the terms: 0.9025 + -1.9z + z2 = 4.8 + 0.9025 Combine like terms: 4.8 + 0.9025 = 5.7025 0.9025 + -1.9z + z2 = 5.7025 Factor a perfect square on the left side: (z + -0.95)(z + -0.95) = 5.7025 Calculate the square root of the right side: 2.387990787 Break this problem into two subproblems by setting (z + -0.95) equal to 2.387990787 and -2.387990787.Subproblem 1
z + -0.95 = 2.387990787 Simplifying z + -0.95 = 2.387990787 Reorder the terms: -0.95 + z = 2.387990787 Solving -0.95 + z = 2.387990787 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + z = 2.387990787 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + z = 2.387990787 + 0.95 z = 2.387990787 + 0.95 Combine like terms: 2.387990787 + 0.95 = 3.337990787 z = 3.337990787 Simplifying z = 3.337990787Subproblem 2
z + -0.95 = -2.387990787 Simplifying z + -0.95 = -2.387990787 Reorder the terms: -0.95 + z = -2.387990787 Solving -0.95 + z = -2.387990787 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + z = -2.387990787 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + z = -2.387990787 + 0.95 z = -2.387990787 + 0.95 Combine like terms: -2.387990787 + 0.95 = -1.437990787 z = -1.437990787 Simplifying z = -1.437990787Solution
The solution to the problem is based on the solutions from the subproblems. z = {3.337990787, -1.437990787}
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