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Simplifying 14x + 13 = 10x2 Reorder the terms: 13 + 14x = 10x2 Solving 13 + 14x = 10x2 Solving for variable 'x'. Combine like terms: 10x2 + -10x2 = 0 13 + 14x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.3 + -1.4x + x2 = 0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -1.4x + 1.3 + x2 = 0 + 1.3 Reorder the terms: -1.3 + 1.3 + -1.4x + x2 = 0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -1.4x + x2 = 0 + 1.3 -1.4x + x2 = 0 + 1.3 Combine like terms: 0 + 1.3 = 1.3 -1.4x + x2 = 1.3 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 1.3 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 1.3 + 0.49 Combine like terms: 1.3 + 0.49 = 1.79 0.49 + -1.4x + x2 = 1.79 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 1.79 Calculate the square root of the right side: 1.337908816 Break this problem into two subproblems by setting (x + -0.7) equal to 1.337908816 and -1.337908816.Subproblem 1
x + -0.7 = 1.337908816 Simplifying x + -0.7 = 1.337908816 Reorder the terms: -0.7 + x = 1.337908816 Solving -0.7 + x = 1.337908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.337908816 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.337908816 + 0.7 x = 1.337908816 + 0.7 Combine like terms: 1.337908816 + 0.7 = 2.037908816 x = 2.037908816 Simplifying x = 2.037908816Subproblem 2
x + -0.7 = -1.337908816 Simplifying x + -0.7 = -1.337908816 Reorder the terms: -0.7 + x = -1.337908816 Solving -0.7 + x = -1.337908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.337908816 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.337908816 + 0.7 x = -1.337908816 + 0.7 Combine like terms: -1.337908816 + 0.7 = -0.637908816 x = -0.637908816 Simplifying x = -0.637908816Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.037908816, -0.637908816}
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