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Simplifying 5x2 + 2x + -8.75 = 0 Reorder the terms: -8.75 + 2x + 5x2 = 0 Solving -8.75 + 2x + 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'. -1.75 + 0.4x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 0.4x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 0.4x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 0.4x + x2 = 0 + 1.75 0.4x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 0.4x + x2 = 1.75 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 1.75 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 1.75 + 0.04 Combine like terms: 1.75 + 0.04 = 1.79 0.04 + 0.4x + x2 = 1.79 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 1.79 Calculate the square root of the right side: 1.337908816 Break this problem into two subproblems by setting (x + 0.2) equal to 1.337908816 and -1.337908816.Subproblem 1
x + 0.2 = 1.337908816 Simplifying x + 0.2 = 1.337908816 Reorder the terms: 0.2 + x = 1.337908816 Solving 0.2 + x = 1.337908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.337908816 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.337908816 + -0.2 x = 1.337908816 + -0.2 Combine like terms: 1.337908816 + -0.2 = 1.137908816 x = 1.137908816 Simplifying x = 1.137908816Subproblem 2
x + 0.2 = -1.337908816 Simplifying x + 0.2 = -1.337908816 Reorder the terms: 0.2 + x = -1.337908816 Solving 0.2 + x = -1.337908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.337908816 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.337908816 + -0.2 x = -1.337908816 + -0.2 Combine like terms: -1.337908816 + -0.2 = -1.537908816 x = -1.537908816 Simplifying x = -1.537908816Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.137908816, -1.537908816}
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