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Simplifying -5x2 + 21x + 4 = 0 Reorder the terms: 4 + 21x + -5x2 = 0 Solving 4 + 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'. -0.8 + -4.2x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -4.2x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -4.2x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -4.2x + x2 = 0 + 0.8 -4.2x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -4.2x + x2 = 0.8 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 = 0.8 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = 0.8 + 4.41 Combine like terms: 0.8 + 4.41 = 5.21 4.41 + -4.2x + x2 = 5.21 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 5.21 Calculate the square root of the right side: 2.282542442 Break this problem into two subproblems by setting (x + -2.1) equal to 2.282542442 and -2.282542442.Subproblem 1
x + -2.1 = 2.282542442 Simplifying x + -2.1 = 2.282542442 Reorder the terms: -2.1 + x = 2.282542442 Solving -2.1 + x = 2.282542442 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 = 2.282542442 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 2.282542442 + 2.1 x = 2.282542442 + 2.1 Combine like terms: 2.282542442 + 2.1 = 4.382542442 x = 4.382542442 Simplifying x = 4.382542442Subproblem 2
x + -2.1 = -2.282542442 Simplifying x + -2.1 = -2.282542442 Reorder the terms: -2.1 + x = -2.282542442 Solving -2.1 + x = -2.282542442 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 = -2.282542442 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -2.282542442 + 2.1 x = -2.282542442 + 2.1 Combine like terms: -2.282542442 + 2.1 = -0.182542442 x = -0.182542442 Simplifying x = -0.182542442Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.382542442, -0.182542442}
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