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Simplifying 20x2 + -14x + -7 = 0 Reorder the terms: -7 + -14x + 20x2 = 0 Solving -7 + -14x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.35 + -0.7x + x2 = 0 Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + -0.7x + 0.35 + x2 = 0 + 0.35 Reorder the terms: -0.35 + 0.35 + -0.7x + x2 = 0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + -0.7x + x2 = 0 + 0.35 -0.7x + x2 = 0 + 0.35 Combine like terms: 0 + 0.35 = 0.35 -0.7x + x2 = 0.35 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 = 0.35 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 0.35 + 0.1225 Combine like terms: 0.35 + 0.1225 = 0.4725 0.1225 + -0.7x + x2 = 0.4725 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 0.4725 Calculate the square root of the right side: 0.687386354 Break this problem into two subproblems by setting (x + -0.35) equal to 0.687386354 and -0.687386354.Subproblem 1
x + -0.35 = 0.687386354 Simplifying x + -0.35 = 0.687386354 Reorder the terms: -0.35 + x = 0.687386354 Solving -0.35 + x = 0.687386354 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 = 0.687386354 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 0.687386354 + 0.35 x = 0.687386354 + 0.35 Combine like terms: 0.687386354 + 0.35 = 1.037386354 x = 1.037386354 Simplifying x = 1.037386354Subproblem 2
x + -0.35 = -0.687386354 Simplifying x + -0.35 = -0.687386354 Reorder the terms: -0.35 + x = -0.687386354 Solving -0.35 + x = -0.687386354 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 = -0.687386354 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -0.687386354 + 0.35 x = -0.687386354 + 0.35 Combine like terms: -0.687386354 + 0.35 = -0.337386354 x = -0.337386354 Simplifying x = -0.337386354Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.037386354, -0.337386354}
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