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Simplifying 10x2 + 20x + 7 = 0 Reorder the terms: 7 + 20x + 10x2 = 0 Solving 7 + 20x + 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'. 0.7 + 2x + x2 = 0 Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + 2x + -0.7 + x2 = 0 + -0.7 Reorder the terms: 0.7 + -0.7 + 2x + x2 = 0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + 2x + x2 = 0 + -0.7 2x + x2 = 0 + -0.7 Combine like terms: 0 + -0.7 = -0.7 2x + x2 = -0.7 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.7 + 1 Reorder the terms: 1 + 2x + x2 = -0.7 + 1 Combine like terms: -0.7 + 1 = 0.3 1 + 2x + x2 = 0.3 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.3 Calculate the square root of the right side: 0.547722558 Break this problem into two subproblems by setting (x + 1) equal to 0.547722558 and -0.547722558.Subproblem 1
x + 1 = 0.547722558 Simplifying x + 1 = 0.547722558 Reorder the terms: 1 + x = 0.547722558 Solving 1 + x = 0.547722558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.547722558 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.547722558 + -1 x = 0.547722558 + -1 Combine like terms: 0.547722558 + -1 = -0.452277442 x = -0.452277442 Simplifying x = -0.452277442Subproblem 2
x + 1 = -0.547722558 Simplifying x + 1 = -0.547722558 Reorder the terms: 1 + x = -0.547722558 Solving 1 + x = -0.547722558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.547722558 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.547722558 + -1 x = -0.547722558 + -1 Combine like terms: -0.547722558 + -1 = -1.547722558 x = -1.547722558 Simplifying x = -1.547722558Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.452277442, -1.547722558}
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