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Simplifying 10x2 + 7x + -20 = 0 Reorder the terms: -20 + 7x + 10x2 = 0 Solving -20 + 7x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2 + 0.7x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.7x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.7x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.7x + x2 = 0 + 2 0.7x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.7x + x2 = 2 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 2 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 2 + 0.1225 Combine like terms: 2 + 0.1225 = 2.1225 0.1225 + 0.7x + x2 = 2.1225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 2.1225 Calculate the square root of the right side: 1.456880228 Break this problem into two subproblems by setting (x + 0.35) equal to 1.456880228 and -1.456880228.Subproblem 1
x + 0.35 = 1.456880228 Simplifying x + 0.35 = 1.456880228 Reorder the terms: 0.35 + x = 1.456880228 Solving 0.35 + x = 1.456880228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 1.456880228 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 1.456880228 + -0.35 x = 1.456880228 + -0.35 Combine like terms: 1.456880228 + -0.35 = 1.106880228 x = 1.106880228 Simplifying x = 1.106880228Subproblem 2
x + 0.35 = -1.456880228 Simplifying x + 0.35 = -1.456880228 Reorder the terms: 0.35 + x = -1.456880228 Solving 0.35 + x = -1.456880228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -1.456880228 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -1.456880228 + -0.35 x = -1.456880228 + -0.35 Combine like terms: -1.456880228 + -0.35 = -1.806880228 x = -1.806880228 Simplifying x = -1.806880228Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.106880228, -1.806880228}
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