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Simplifying 3s2 + 7s2 + -18s + -42 = 0 Reorder the terms: -42 + -18s + 3s2 + 7s2 = 0 Combine like terms: 3s2 + 7s2 = 10s2 -42 + -18s + 10s2 = 0 Solving -42 + -18s + 10s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -9s + 5s2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -9s + 5s2)' equal to zero and attempt to solve: Simplifying -21 + -9s + 5s2 = 0 Solving -21 + -9s + 5s2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -1.8s + s2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -1.8s + 4.2 + s2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -1.8s + s2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -1.8s + s2 = 0 + 4.2 -1.8s + s2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -1.8s + s2 = 4.2 The s term is -1.8s. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8s + 0.81 + s2 = 4.2 + 0.81 Reorder the terms: 0.81 + -1.8s + s2 = 4.2 + 0.81 Combine like terms: 4.2 + 0.81 = 5.01 0.81 + -1.8s + s2 = 5.01 Factor a perfect square on the left side: (s + -0.9)(s + -0.9) = 5.01 Calculate the square root of the right side: 2.238302929 Break this problem into two subproblems by setting (s + -0.9) equal to 2.238302929 and -2.238302929.Subproblem 1
s + -0.9 = 2.238302929 Simplifying s + -0.9 = 2.238302929 Reorder the terms: -0.9 + s = 2.238302929 Solving -0.9 + s = 2.238302929 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + s = 2.238302929 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + s = 2.238302929 + 0.9 s = 2.238302929 + 0.9 Combine like terms: 2.238302929 + 0.9 = 3.138302929 s = 3.138302929 Simplifying s = 3.138302929Subproblem 2
s + -0.9 = -2.238302929 Simplifying s + -0.9 = -2.238302929 Reorder the terms: -0.9 + s = -2.238302929 Solving -0.9 + s = -2.238302929 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + s = -2.238302929 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + s = -2.238302929 + 0.9 s = -2.238302929 + 0.9 Combine like terms: -2.238302929 + 0.9 = -1.338302929 s = -1.338302929 Simplifying s = -1.338302929Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.138302929, -1.338302929}Solution
s = {3.138302929, -1.338302929}
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