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Simplifying 5x2 + 21x + 7 = 0 Reorder the terms: 7 + 21x + 5x2 = 0 Solving 7 + 21x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 4.2x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 4.2x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 4.2x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 4.2x + x2 = 0 + -1.4 4.2x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 4.2x + x2 = -1.4 The x term is 4.2x. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2x + 4.41 + x2 = -1.4 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = -1.4 + 4.41 Combine like terms: -1.4 + 4.41 = 3.01 4.41 + 4.2x + x2 = 3.01 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 3.01 Calculate the square root of the right side: 1.734935157 Break this problem into two subproblems by setting (x + 2.1) equal to 1.734935157 and -1.734935157.Subproblem 1
x + 2.1 = 1.734935157 Simplifying x + 2.1 = 1.734935157 Reorder the terms: 2.1 + x = 1.734935157 Solving 2.1 + x = 1.734935157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 1.734935157 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 1.734935157 + -2.1 x = 1.734935157 + -2.1 Combine like terms: 1.734935157 + -2.1 = -0.365064843 x = -0.365064843 Simplifying x = -0.365064843Subproblem 2
x + 2.1 = -1.734935157 Simplifying x + 2.1 = -1.734935157 Reorder the terms: 2.1 + x = -1.734935157 Solving 2.1 + x = -1.734935157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -1.734935157 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -1.734935157 + -2.1 x = -1.734935157 + -2.1 Combine like terms: -1.734935157 + -2.1 = -3.834935157 x = -3.834935157 Simplifying x = -3.834935157Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.365064843, -3.834935157}
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